The legal drinking age in the province of Manitoba is 18 years. If you look 20ish, you will be asked for ID when buying alcohol or entering a pub. It is illegal to drink alcohol in public other than in a licensed premise. You are allowed to drink in private. In your private residence, hotel room or camping spot, etc.
Regarding drinking and driving, Manitoba has very strict laws about this. There are two levels where if you are caught, you will be in trouble. If you have .05 % alcohol in your blood, you earn a ticket, and you are not allowed to drive your car home. If you have .08 % alcohol (or more) in your blood, you can lose your vehicle, your driver's licence and I don't know what else.
To buy alcohol, there are provincially-run and owned) Liquor Commissions - stores that sell liqour, wine and beer (not refridgerated). They are somewhat convenient (open Mondays to Saturdays) -- not as convenient as it would be if we could buy wine in a grocery store.
Many hotels also have a 'beer store'. They tend to have cold beer. Prices are the same no matter which type of store you buy your beer from. There are also some private wine stores, but they tend to sell only the high-end stuff.