I don't think you'll have any probs crossing the border into Canada, even with your laptop and chase gear. While it may depend on where you cross, I've found (no anti-American slurs intended) that Canadian border personnel are a bit easier to deal with than their counterparts.
Every year, I cross the border at least three or four times while chasing. I've even crossed over into America and only stayed three hours. We told them what our visit was for (that big storm over there!), and he wished us good luck and sent us on our way.
While I don't think anybody is going to confuse Manitoba in June with Oklahoma in April, or whatever, we do have quality storms here, as the record shows (COD chases here, also). Another plus is that you won't run into the circus show convergences that you get in the central or southern Plains.
Whenever possible, try to cross at Pembina, ND/Emerson, MB. It is an efficient crossing, and if you go from Mon.-Thurs., it is often pretty quiet.
To answer Justin's question, weather radio works the same way here as it does south of the line. Information and forecasts are furnished by EC via WeatherRadio Canada, Winnipeg frequency is 162.55 MHz, station identifier XLM538.
Enjoy your stay.
John
VE4 JTH