Well...
I don't use deodorant, mostly because I don't like people who smell like perfume store. And it feels... uncomfortable. I take shower at least once every two days in cold time of the year (10 months out of 12 here), and every morning if temperature is over +20C. I mean - not just jump under shower and get myself wet, but wash carefully.
I hate people who have strong body odour, especially in the underground, where sometimes you get pressed agaist someone's sweaty fat body...
I wonder why people who work physically usually smell better then office workers.
Another intersting thing that you probably don't know: every year we have hot water turned off for 3 weeks. It's a usual "profilactics" for the pipe system. You know, you can get in a big trouble if water or heating pipes freeze and blow up in winter when it's below -20C. In my flat they will turn hot water back on Monday. I live in the North of Moscow, not far from water "inlet", and cold water is really cold - I can't wash under cold shower when it's about 8-10C. My Father lives almost in the center, near University, and in his flat cold water is 15-20C in Summer, so I can take a cold shower easily. For over two weeks now I have to boil a bucket of water and wash almost like a cat

or go to my Father or some friend who still has hot water. After Monday I expect some guests visiting me to take a bath...
Russian hygienic tradition is really old.
Banya (Finns call it Sauna) was a tradition for centuries. Russians went to banya at least once a week when in Europe people were washed twice in their life: when born and after they died. Now banya is more like a social event, having good time.
As for "smell of the Russian soldiers" - try to live in trenches for a month or two without changing your clothes or underwear and without any chance to wash at all. I bet Soviet soldiers could smell nazis too.