Well if your looking for MX tracks there are several open to the public and many private if you get to know the right people! The public tracks that the Manitoba Motocross Association race on with listed open practice times are:
Beausejour - Tuesday and Thursday 6pm-dark, Friday 6pm-dark (85cc and under only)$10 big bikes, $5 85cc and under
Grunthal - Open all day Wednesday, Friday and Saturday $10 all bikes.
Altona - Tuesdays noon - dark, no fee.
Morden - Open 7 days a week, $5
Firdale - Open 7 days a week, $10 almost never anyone comes by to collect.
Brandon - I think they are open 7 days a week, not sure on the fee never driven out to practice there.
Melita - We raced there this year but not sure about any practice time available.
For more info on MX in Manitoba and for directions to all the tracks check out
http://www.manitobamotocross.com
As for trails I haven't done much trail riding but the Seddon's Corner and Libau area's are packed full of sand pits and snowmobile trails that go for miles. I've also heard there is some awesome sand dunes in the Portage/Carberry area but have never searched them out.
What part of the province are you in?