One site said that 'Winster Gallop' is the first session tune we learn. That surprised me, because I know a lot of famous tunes, but I'd never heard of 'Winster Gallop' till today.

Leeneia, that's because your not in the UK. Over here it is commonly among the first session tunes that are learnt, along with Jamie Allen and Salmon Tails (for me at least). As a result many folk get sniffy if you start it in a session which is a pity because it's a good tune.