I encountered the same issue when KoL told me to find an "Orcish Frat Boy". It ended up being the Orcish Frat Boy (music lover), so in the code for setting the daily properties I added a little breakout section for fixing ambiguous monster names into specific ones, with the idea that more monsters would be added as we found more of these situations.
So what we need to know in your case is: which monster was the right one? Then we can fix the script to hunt the correct snowman.
Optionally, it may not always be the same monster, in which case we would need to use a list of monsters that match an ambiguous name, trying any of them until one of them gives us quest progress.