Rain and snow do not stop people from bicycle commuting.
A lot of people use seat covers to keep their bicycle seats dry and protected, thus the brilliance of a marketing giveaway- free printed seat covers.
Lots of people use the freebies, but others are more fashionable and/or less compliant in 3rd party advertising.
There are designer seat covers and DIY plastic bag projects.
Here's a quick selection.
This is a bag from the local supermarket.
Plastic with lace edgings.
Ceramic pets approve of this designer seat cover.
Bike cap. Excuse me.