I have done this and would probably not do it again -- it takes some awareness and some re-training to go from coaster brake to being able to backpedal freely. I'm on my third winter on the coaster-brake bike and still have trouble coming to a stop with the right pedal in the "take-off" position. But then I'm not very coordinated.
The upside of the coaster brake, and why I still use it, is the simplicity for winter riding. In rust belt winters, everything corrodes and gets messed up. So there's one less apparatus to worry about, plus the chain won't freeze up like the brake cable could.
I searched high and low for a steel mountain bike with horizontal dropouts. They're like hen's teeth. Specialized bikes up until 1993 or so qualify, so I got a Rockhopper.
My last winter bike was Cannondale hybrid, with horizontal dropouts like all aluminum bikes I've ever seen, and there I used a calculator similar to what @iamkeith is recommending. It gets futzy, and the result won't be gospel, but this type of calculator is essential to figuring out a chainring/sprocket combination that works. A little trial and error might be necessary. Expect maybe 4-500 miles of wear before the chain elongates enough to become a problem.
Fun fact, after the chain comes off, you got no rear brake. So make sure you have one in front also.
As @Bill Lindsay alluded to above but didn't spell out: Coaster brakes and chain tensioners don't really mix. Whatever slack is in the system needs to be taken up before the braking starts.
Also, by the time you add the tensioner, just get one that shifts ;)
The whole thing seems like trouble; nothing wrong with coaster brakes, just use a frame the works with you, not against you.
cheers -mathias