Rain has begun, and will continue through the night.
It is looking likely that we will see rain beginning to mix with wet snow overnight with temperatures dropping close to the freezing mark. It shouldn't accumulate to much; and even if it does, it would just melt tomorrow with the warm ground and some sunshine. There is a higher chance you wont be seeing snow on the ground in the morning.
I'm saying 5 to 10 mm around Winnipeg with this system, though there could be some locally higher amounts near 15 mm in some heavier bands since there could be some embedded convection.
Sun will begin to peak out tomorrow, but it wont be a full blown sunny day, with much more cloud than sun. Thursday looks sunnier, but with some high cloud.
It will be rather cool for the next few days, until Saturday. Sunday and Monday will feature a nice warmup back into at least the mid teens as a ridge builds over western Canada. Just how long the warmup will last is yet to be determined at this point, but it does not look like it will be here to stay for long at this point unfortunately..