Saint Petersburg here.
I'd say in winter and early spring bring warm clothes and warm boots. Be prepared for ice on the streets, so something not slippery is a good idea. Definitely have mittens or warm gloves. Last winter I saw some tourist in a cafe with 2 jackets on (prob. autumn ones), he must have been really cold.
Snow usually melts in March-April.
I'd say in the spring and summer be prepared both for cold weather and warm one. April in particular could be quite warm, even warmer then May. In the beginning of May it could be quite cold, so called "bird cherry tree blossoming cold" - when it blossoms it usually gets colder for a week or so.
June could be quite cold and rainy. In the end of June it usually gets better and warmer. Even last summer (2010) when July was REALLY hot, second and third weeks of June were quite cold and rainy.