Crown
I myself have not had to make a crown like this, and I actually forgot he had rubies on it before google-ing the picture.
To me, it'd be a couple layers of poster board, rolled to measure and fit snuggly on your head, stapled together or whatever you want to do to attach the ends, cut evenly for the points, make some lightweight rubies out of model magic formed around a pin of some sort that you can secure on the other end of the posterboard.
For the rubies, find something you can snap into the posterboard, get some white model magic [they sell it at literally any hobby store], form basic ruby shapes around that. Try not to leave any creases because they will crack. Let them dry for like, a week. Because you're making such big shapes, it takes longer for the MM to dry completely and get all the moisture out. Once those are COMPLETELY, fill any cracks [unavoidable pretty much] with wood filler [find one that does not expand], and sand with a lowish grade sandpaper until you are satisfied with the edges.
Get some nice ruby red paint and paint probably 3 good layers of that, find some Mod Podge [it's a sealing glue kind of thing, the glass finish may give it the shine you'd want for the rubies] and paint a couple layers of that and let them dry completely [don't worry, it dries completely clear].
Keep in mind I haven't done this before so you may need to tweak it accordingly.
Nose
I believe you could also make this out of layered posterboard, make it 3D, and attach it to a string that would probably be mostly hidden by your beard. Try to use an invisible elastic one if possible. Paint the nose in the color of your facepaint [talked about later on]. There are definitely other methods though.
Beard
You could either make it out of faux fur, a collection of wigs [i do not know how to do this], or probably find an actual Santa costume beard online.
Robe
You probably need to actually make this robe dress thing unless you find the XXXXXL long sleeve shirt at Goodwill. I do not know how to sew at all.
Eyebrows
Faux fur strips that are applied with body adhesive if you want to be more realistic than just using body paint.
Teeth [opt]
Completely optional but they have costume veneers you can use to achieve his sharp pointed teeth.
Cannibal - Vampfangs Pro FX Veneers
Vamp Fangs is literally my favorite site for fangs, but if those aren't sharp enough for you, you can also make them out of sharpened and painted fake nails and glued to your teeth with denture glue.
White out mesh contacts [opt]
Even more optional than the fake teeth, it just really adds to the costume. If you need a prescription to wear contacts, do not get these ones I'm linking you.
White Out Contact Lenses | White Mesh Contact Lenses (Pair)
These do not come in perscription, that's why they're so cheap.
Vamp Fangs also has perscription contact lenses but you need to have your doctor fax them info.
Regardless, if you don't want to, or don't feel like it, don't have to.
Blue Face Paint [opt]
Aight, so, I haven't seen literally any Ice Kings that did not go through with the facepaint. Some opted out so they could grab stuff and not worry about smudging and it coming off after a while and used blue gloves to match, but yeah.
So Ben Nye.
I used the stuff before for my troll cosplays and it works really well WHEN APPLIED PROPERLY.
First off, you probably want 1 thing of Sky Blue Ben Nye Creme Liner.
Creme Color Liners Ben Nye
Since you are only doing your face, you don't need much. If you know anyone who knows more about make up than I do [which is a lot of people, actually...], talk to them about what you can use to highlight and sharpen your face, because I do not know what colors to use with blue. I'd imagine white and a darker blue, but that's just me.
Anyways, so you'll also need powder and finishing spray. You can get both on the same website, since you're using your face I recommend them both. If you were using it on your arms or w/e it'd be fine to just powder with baby powder [corn starch only], but I don't trust baby powder on my face for a long time, so, yes, Ben Nye powder and Finish Seal Spray.
Other things you'll need are cosmetic wedges, mascara [though the powder will make your eyelashes white so maybe just get a transparent one??? ono"], a powder puff [also sold on site and in most cosmetic stores], chapstick, cosmetic primer [I use Loreal], and brushes [specifically a powder brush to brush off excess powder]
There are also other brands like Snazaroo and whatnot as well. Youtube probably has some tutorials of people who've cosplayed him, try to find those. uwu
Wash your face completely, this works best after a good shower and your skin is clean and dry. Put in any teeth, contacts, etcetcetc BEFORE applying! AND DON'T WEAR THE ROBE WHILE PUTTING THIS ON, YOU'LL GET POWDER EVERYWHERE.
Now, get your real hair back [I suggest a wig cap, especially since you'll be wearing the beard hair combo, so get a blonde wig cap], and apply the primer to your face with your finger. You only need a spot for each area, it goes a long way. Those being: Both cheeks, nose, forehead [may need two], chin, etc. Smooth it all completely. You should be a pretty lady when done. Put on some chapstick to keep your lips moisturized.
Moving onto the main purpose of this. Take your sky blue and a cosmetic wedge, and start applying this to your face in an even coat. You may need to do two or even three depending. DO NOT SMEAR! It will show in your photos and it just turns out messy, especially when applying the second coats. Dab it on! Be patient and cover all the areas of your face and neck [you may need help with the back], this takes a while.
This is the part that I'm still a bit eeeh on because I did this with grey, white, and darker grey when I did my troll skin. I was also trying to look YOUNGER not 1000+ years older and blue...
Once you have all the areas covered, take the white or lighter blue [make up experience right here idfk], and highlight the bridge of your nose [if you aren't using the fake one], but I think you need more darkened areas tbh...
Contour the sides of your nose [again no fake nose] with the darker color, also hitting the cheekbones [suck in like a fish to find your cheek bones. follow that with the darker color.], and maybe even make some creases on your forehead and make the circles under your eyes a bit exaggerated.
You could probably also use the make up to make your eyebrows white.
Once this is all done and you're happy with it, take a bunch of powder and put it on to your powder puff. Literally dab it EVERYWHERE on your face until it isn't sticky anymore. You'll again probably definitely need some help with the neck. Once that's done, you'll be covered in powder but don't worry, after brushing it off with your puffy brush [kabuki or blush brush idgaf neither does the powder], the color will be in tact. Your eyelashes will probably be white, you probably want to do something subtle about that as opposed to what I did and just put on colored mascara. Maybe transparent mascara just to clean it off.
You can probably work on making yourself look older with the magic of make up that I do not know how to do at all but, yes that would be in this step, also anything eye make up or whathaveyou here as well. Personal preferences, etc.
Next, the Final Seal Spray. This stuff will ensure that your make up will not come off. Spray a bit ahead of you and move into the mist cloud with your eyes closed. Do not spray directly onto your face [spots will show and it will make everything look shitty] and doooo noooot get this in your eyes it hurts like a motherdiddlyer. Do this one or two more times just to make sure it's even. Do this everywhere that is makeup'd and on your neck.
Then put on the giant robe thing, your nose and beard thing, crown and you should be done!