Here's a really cool website you can play around with. I just checked off only the Beef box and 21 farms come up. Then you can see who is behind these farms and what they offer by clicking on their links. There's one called Howpark Farms near Brandon that have grass fed beef (and more) for sale.
http://www.directfarmmanitoba.ca/farms
There's tons on this website from finding Manitoba farms that offer meat, poultry, dairy, eggs, veggies, fruit, grains, trees, seeds, Fibres, personal care stuff, CSA programs, Farmer's Markets, U-picks, etc.
Personally I love the products from Henry Meats (2.5 miles North on Prov. Rd. #270 off Trans Can #1 West of Brandon).
They also have a public FB page anybody can check out, whether your on FB or not. I can't 100% for sure say they offer grass fed beef, but I know their roasting chickens are farm raised, free range, not force fed, antibiotic free, no additives, etc. so they do care about that kind of stuff. Might be worth a call.
In the meantime, you might find a nice match on the above website.