I was there in April and there was still a lot of snow off to the side where it had been plowed from the streets. Also, the city of Moscow has several large central heating plants which then distributes steam to other buildings, many often several blocks away, with much of the distribution network placed above ground and you could see where steam was venting from leaks and such. But overall, the weather, while it was overcast for most of my 4 or 5 days that I was there, it was never 'cold'. You needed to wear a coat or jacket, but you didn't need gloves or a hat, although almost everyone in the city seems to wear hats, but I assume that is just part of their normal garb and after all it was sort of 'between seasons', it was technically Spring, but being Moscow, is was still a bit more Winter than anything.
That being said, if your plans are to be there in the Summer, while I've never been there myself during that time of the year, I understand that Moscow can get brutally hot in July and August, and even into September.
OCU