Will fish gather by the warmer water in the winter months, or is that hot spring water no good and fish avoid it? Maybe oxygen content changes or other? 

I would expect fish to relate to the warmer water temps, but I think the oxygen-poor water from a hot spring would certainly affect their proximity to it.  I’m guessing there is a ‘sweet spot’ where the water is marginally warmer and oxygen from the lake water is available. 

Of course there is always the chance that the hot spring is releasing toxic dissolved gases, and it could be a dead zone.

Yes, as long as it isn't toxic to them for one reason or another... prior to 9/11 there were all kinds of warm water discharges you could fish in the Winter here in the Great Lakes, anywhere you still can, great fishing in the colder months... Not quite the same, but maybe more toxic in some ways lol 

I have noticed fish will self regulate 

I like fishing transition, ether warm to cold or vice versa, just got to find them. 
Never fished a hot springs before, but we have a salt spring here.  Which stays warmer in the winter, and they will get close to mouth or move according to what they want. 
 

All spring water is 50 to 60 degrees and warmer then winter cold water.

The cold water is very high in dissolved oxygen (DO) and readily mixes with warmer spring water. Hot spring water is possible but not common. You will see heavy fog around a hot spring in the winter and light mist fog with normal spring water in the in the cold water period.

Tom