Recently the cartridge to our bathtub was changed (moen) and now there is no cold water coming from the bathtub faucet, only hot water.

Sounds like you disturbed some minerals built up on the pipe walls and now it's blocking the cold water inlet ports on your cartridge. Shut the water off and pull the cartridge. Check and clean the inlet ports. Before you button up turn the water back on for a few seconds to flush out the supplies. Reassemble and test. Better now?
Good luck, Tom