Hello Dess-tin,
Winter in Kyoto: Though snow can usually be seen on the surrounding mountaintops it rarely snows in Kyoto now. Accumulation is a rarity and only lasts for a few hours.
Bicycles in Kyoto: Yes, bicycles are a primary mode of transportation for many residents of the city. Sightseeing in Kyoto by bicycle is an excellent way to experience the city. Kyoto is a bicycle friendly city, ALTHOUGH, you must be careful parking a bicycle in the downtown areas, especially near stations and in the Shijo, Sanjo areas. Bicycles are impounded on a daily basis. Usually the impounding is done in the A.M. and not done on weekends. (I could be wrong about this or it could change any time.)
Rental: Try Kyoto Electric Bicycle Rental “Kyo no Raku Chari”, I haven’t rented a bicycle here before but I have heard good things about Kyo no Raku Chari. They have an English language website and it is conveniently located just off of Sanjo Street, near the Sanjo-Higashiyama intersection
Kyo no Raku Chari homepage:
http://eng.rentacycle.jp/
Kyo no Raku Chari map:
http://eng.rentacycle.jp/mapinfo_e.html
Used Bicycle Purchase:
If you are going to be in town for a few weeks or months, you can often purchase a used bicycle in good condition at a reasonable price. There are numerous shops that sell them. Just ask around in your neighborhood.