For Winter do not forget a hat, a scarf, mittens (no leather gloves!), sweaters, a really good warm jacket and warm boots. It is interesting, that even in Winter Russian people still think about how it will all look together and are they still look fashionable.
For the Summer the most important clothing item in your luggage should be comfortable shoes. Moscow and Saint Petersburg are made to be explored on foot. You'll end up walking for 6-8 hours a day on average. Pack something not just purchased, that won't make a walk around the city a struggle.
Do not forget a shawl and a skirt for those days when you are planning to visit churches. Women have to wear skirts below the knee and put on shawls on their heads when entering a church, men have to remove any hats/caps. Some of the most touristy churches and temples have skirts and shawls you can borrow at the entrance.
For the going out do not forget something nice, but rather casual, except jeans, that are not recommended to wear in such places as Theaters and restaurants in the evening.