Hi Sambamuel, I think it was an original concept but the theme and functionality let it down a bit. From what I have heard and seen recommended by many peers is to keep things simple (until you are ready to add complexity).
Firstly Suicide or Snowacide (though amusing in a black comedy sense) probably if meant seriously may not float many peoples boats. I think it probably needed some story and context as to why the snowman was trying to melt himself. This would have also helped with understanding the game mechanics and the motivation of the player character. As it is a touchy subject if I was to attempt I would try a humour route (perhaps the Snowman was sad Christmas was over or something).
Instructions in game to get you doing the right things - like a playable tutorial would have really helped as I enjoyed wandering round and the setting but was quite lost until I stumbled into a speedy Snowman (at first I thought they came through the windows to attack me). I found it weird my gun didn't do any damage and the more so when he sped off lol.
I think overall it was a tricky concept as the environment felt large and perhaps (although I cant think of any of the top of my head) more obstacle or tasks (maybe collectibles would have helped the fun factor.
I think its great you asked for feedback and hope I have helped a little (I just have been going on the Jams for about a year so I am sure there will be wiser advice ).
If possible can you give some feedback on mine? as like it seems you are finding along with experience it is one of the best takeaways we get from doing jams.
Keep up the jamming, and merry Xmas,
Rico