I figure getting a saddle damp is no big deal, but I don't want it just soaked every day, so I keep a cover on it full-time. I get the impression the covers are mainly made for when you leave a bike out in the rain, but they work fine for riding, too.
Oh, even if it didn't affect fit, soaking a saddle in sweat every day would surely make it stink in a hurry.
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"be careful this rando stuff is addictive and dan's the 'pusher'."