Hypothetically speaking, since I don't know what deer it is(looks like caribou/reindeer) or where it is.
If within 20 yards, I'd hit it with both barrels of my 20 gauge Howdah pistol firing 350 grain .51 cal round balls. He isn't going anywhere due to about 50 grains of fffg propelling each ball. My POA wold depend upon the range, load, and shooting characteristics of the gun.
If further than 20 yards, I'd either anchor it with my DGW .50 cal Tenn Mtn Rifle flintlock, with about 70 grains of 2f and a PRB or 80 grains and a Lee REAL bullet.
OR, my TC Renegade or New Englander .50, with about 80 grains 2f and a TC Maxi Hunter, cast by me.
I'd aim for the heart/lung/shoulder area. Unless I could get a headshot, since I cant afford to get the head mounted, I'd just use the antlers for accessories, handles, buttons, etc.
Is Santa gonna be mad at me for shooting Rudolph?
Or would I get my gun and vehicle confiscated and lose my hunting license/have to pay a fine for shooting a deer I wasn't legally allowed to shoot? Hypothetically speaking, of course.
I seriously think shooting that one would get me on Santa's permanent naughty list.