Well I'm a MB dad not a mom (4 girls!) but thought I'd reply to your message anyway. :)
I've been looking for Winnipeg sources as well, but I don't think there are any dairy farmers selling raw milk in Manitoba. I would love to join a Manitoba-based cow-share program if there was one.
I've heard that it is legal to sell unpasteurized cheese in Canada as long as it's been aged a certain amount (60 or 90 days?) so you may be able to find that. Frig's Natural Meats website says they sell unpasteurized cheese.
I've heard that there are lots of Manitobans driving down south and purchasing raw milk in Minnesota. You can apparently bring back $20/person worth of raw milk for personal use, without incurring any duty/tax. Minnesota based raw milk suppliers can be found here: http://realmilk.com/where3.html#mn (but I haven't called any yet). There are also a couple North Dakota ones listed.
Finally, there are other dairy farms in Canada that will let you join a cow-share program and ship the milk all the way to Manitoba. In fact I found one in BC that apparently does already ship to someone else in Winnipeg!! http://www.wildthingorganics.com/ I emailed the owner and am considering potentially joining the program ... but it's fairly expensive and I haven't made up my mind yet. (It's possible some Ontario-based farms might also ship their milk.)
Let me know your thoughts, and what you've found in your search. If you're interested I can provide my email address, there might be ways to help each other out.