I have been riding a Gates CDC (not Centertrack) belt drive for almost a year now. I have ridden my bike in various weather conditions and temperatures ranging from over 90℉ to under 0℉. I have ridden through a variety of snowy conditions, including a foot-and-half of fresh snow on a few occasions, but more commonly mixed snow/ice/slush conditions. I have encountered two major problems in winter conditions so far.
The first problem is changing tension. I use the Gates iPhone app to check my belt's tension. I have noticed that, if the belt is tensioned properly at about room temperature, then the tension in the belt decreases below the recommended tension range when the ambient temperature drops below about 20℉. I have noticed problems with the belt drive when tension is too high or too low, including excessive noise, skipping, and misalignment leading to dropping the belt from the sprockets. Therefore, I found it necessary to retension the belt slightly in the beginning of the winter and again at the end of winter. I'm not certain yet if the weather-related change in tension is caused by frame shrinkage (I suspect this is the case - my frame is aluminium) or by another factor.
The second problem is getting snow in the drivetrain. Under certain winter weather conditions, the belt will drop from the sprockets. I've had this happen on several occasions, and it's quite annoying, as there's not much you can do when you're on the road besides remount the belt and pray it doesn't happen again on your ride (spoiler alert: if the belt drops once, the belt will get dropped again). However, this does seem to require the perfect storm of conditions: you need the belt tension to be low (possibly because the temperature is low - see above), and you need very heavy, wet snow that sticks to the components of the drivetrain. When the snow and cruft starts building up on the sprockets and belt, the liklihood of dropping the belt increases dramatically. The solution to this problem seems to be to increase the tension of the belt, though I found it necessary to take care not to increase the tension too dramatically, as an overtensioned belt can be very noisy and create a lot of resistance in the drivetrain.
Overall, with winter weather in the mix, I've found that the belt is not the universal, maintenance-free drivetrain that Gates claims it to be, though with a little care, it does require less frequent attention than a chain-based drivetrain.