There's obviously a plethora of dim sum places in Vancouver but IMO the ones with carts are a becoming a rarer breed with many using the menu card system now.

Just to add a bit more detail to the ones already listed for Vancouver that I'm a familiar with a bit and a couple of more (without prejudice from my impressions of them)...

• Pink Pearl (Slight drive outside of Chinatown): Large to huge restaurant (>500 people). Mid to slightly higher end expensive
• Sun Sui Wah (Main street location): Fairly large restaurant (about 400 people - rough count from a wedding we went to last year). Higher end expensive.
• Floata (Chinatown location): Flippin' huge restaurant (~1000 people). Mid end expensive. Haven't been in a while but I thought they did do carts.
• International Seafood Restaurant (East Vancouver): Medium sized restaurant (~250 people). Inexpensive.
• Golden Phoenix (East Vancouver): Small restaurant (<100 people). Inexpensive. Haven't been in years so don't know if it still does carts.
• Dai Tung (East Vancouver): Small/Med restaurant (~150-200? people). Inexpensive. Haven't been in a few years for dim sum so don't know if it still does carts.
  
• Kirin (various locations): The ones I've been to don't do carts. Large (~300 people). Expensive.

You might be able to identify some more dim sum places with carts from DineHere.ca.