We don't usually start to "feel" the break in the weather until about mid-March. That's when the day-time highs will typically get to above 0 deg. Celsius (freezing), and so you know from the warming weather that spring is coming. But, we look at several different temperatures; the day time high, the night time low and the wind chill factor.
Just because the day time high peaks a little higher than 0, like 1 or 2 degrees, doesn't mean that there's much of a change in the amount of snow you see around. That's cuz the temperature throughout most of the day is still well below 0, and so there's no serious melting going on.
"Spring" doesn't actually feel like it's arrived until mid-April or so when the night time lows inch above 0. That's when the snow melt continues 24/7, (albeit slowing down at night) and you can see a visible difference in the amount of snow from day-to-day, and a corresponding increase in the water level in the river(s). Winnipeg is located at the junction of the Red River which runs from south to north and the Assiniboine River which runs west to east.
Minnesota can feel colder than Winnipeg. How cold "it feels" doesn't just depend on the outdoor temperature. It all depends on how quickly heat leaves your skin. The faster heat leaves your skin, the colder "it feels". And, wind plays a very important role in removing heat from people. If it's a calm day, then the air around your skin will warm up a little, and it won't feel as cold. If it's a windy day, that heat gets carried off with the wind, and it feels colder. We call that effect the "wind chill". So, you might hear on the radio someone saying "It's -14 deg. Celsius outside, but the wind chill is -26 degrees C."
(How cold "it feels" is dependant on how quickly heat leaves your skin. This is also why it can be 65 degrees outside, but if you wade into 65 degree water, it'll feel very cold. The temperature of the water is the same as the air, but water absorbs heat 15 times more quickly from your skin than air does, and so 65 degree water will feel much colder than 65 degree air.)
That means that the actual temperature is -14 deg. C., but it feels like -26 degrees because of the wind.
So, depending on the temperature and the wind, Minnesota can feel a lot colder than Winnipeg.
Here's what's happening right now, and what's forecast to happen over the next several days in Winnipeg:
Winnipeg, Manitoba - 7 Day Weather Forecast - Environment Canada