He wouldn't require water to gain weight....
And yes if he absolutely had too, he could live off eating snow (obviously not ideal, but it could be done)
you said he was still nursing so if he had a few chomps of snow here and there, yes that could hydrate and quench his thirst enough that he wasn't interested in drinking...so don't blow off someones suggestion as to why he may not be drinking so quickly

People are only trying to help
But it sems he has started to drink so that is good news. So now you don't need to give him a bottle, as he needs to continue drinking on his own.