Do you operate in Canada too?

For those American independent o/os who own their own trailers, do you operate in Canada too? I'm not sure what the exact term is, but do some American independent o/os with their own trailers register or licence their trucks and trailers to be able to go in Canada too? If so, how does that affect the insurance premiums, crossing-the-border expenses, taxes, and other fees you pay? Thank you.