I was on a 737 that landed on a snowy runway in northern Finland the other day. We had to wait around 30 minutes to land as they were waiting for it to stop snowing and then for them to clear the runway. The landing was fine but it felt like they used a lot of reverse thrust when landing. Admittedly, it's been 10 years since I last flew, but it got me wondering; in the event of such conditions, would a pilot use reverse thrust more than wheel braking?
On a 737, you have essentially two detents for reverse thrust, which for lack of a better term you could call "normal" and "maximum". You can use levels of reverse thrust other than that by raising the reverse thrust levers to some intermediate position, but the performance numbers are all predicated on either no reverse thrust, normal detent, or maximum.
The condition of the runway absolutely affects how effective the wheel brakes are, and when there is a lot of snow coming down -- even with a freshly plowed runway, you really don't gain much by using less reverse thrust than you have available. Plus, if anything bad were to happen, it's easier to explain yourself when the flight data recorder shows that you went immediately into max reverse thrust right after touchdown & had the anti-skid cycling all the way down the runway -- you used everything you had available to stop the aircraft.
On a long, dry runway, you have lots of choices you can make. You can use reverse thrust and a long rollout to minimize brake wear; you can use no reverse thrust (if your airline permits that option; not all do) and more wheel braking to minimize noise -- which I've experienced at Frankfurt in the early morning; or you can use a good bit of brakes & reverse thrust to make an early turnoff from the runway -- nice if your parking spot is closer to the approach end of the runway than the departure end of the runway.
With contaminated runway conditions, those options boil down to, let's get this thing slowed way down as early and as certainly as we can. Quiet isn't so much of a concern, brake wear isn't so much of a concern, taxi routing isn't so much of a concern; we'll use all the tools we have to reduce all the risks as much as we can.
So yes, you could well see more thrust reverse being used on a snowy day than you might see on a clear, dry day. The relative contribution of the reverse thrust and the wheel brakes is one of those engineering questions that needs a lot of specific numbers to answer... just how slick is the runway? (Braking will be less effective, so the contribution of the TR's will be higher.) How cold is it? (Reverse thrust is more effective in cold air -- more thrust.) How quickly did the braking get into the anti-skid cycling? (You somewhat expect the anti-skid to be cycling on a snow-covered runway -- that means you're getting all you can out of the wheel brakes, given the friction with the runway they have to work with.) And etc. As a pilot, the salient point isn't that X% of my stopping came from the one and y% came from the other; it's that we used them both & reached the gate, on time & with zero groundspeed!