A nice attempt and I think the heart is in the right place, but I'd say it unfortunately falls short of being a good fangame by missing some critical aspects.
For one, the great thing about Henry Stickman games I find is how animated and lively everything is, and that includes the buttons which would usually play out an animation or a sound when you hover over them: the buttons in this, unfortunately, were very lifeless and stiff with no such pizazz or life to them.
The scenarios that played out weren't that unique or inventive either, most just being a silly one-note gag that didn't really use the whole winter situation to enhance it or have the craziness and escalation that most Henry Stickman gags did. Heck, you had two jack-in-the-box scenarios that were practically identical, and then two phone scenarios that were literally identical as they were just copy-paste!
All this just made the game feel rather lazy: just felt like the list of options was bloated with a lot of fluff: I'd say the only ones I really liked were the the jacket, the load save, the teleporter, the go deeper, and maybe the cheese/bomb/radio. It's not all bad: like I said, there were some decent options in there and I liked the stickman animations and such as they looked very authentic, so I think the heart is in the right place: hopefully I don't sound like too much of a jerk, just want to point out some of the hidden aspects that really could help enhance the experience if you revisit.