I can't comment on cost, but yes. As you describe it, it sounds to me the location of the new hood would be on an exterior wall. This is easy to vent to the exterior.

As a general observation, this should be relatively easy. You should have several options. The simples, as kirkhall suggests, would be to vent the hood through the exterior wall directly out the side of the house. That has the advantages of being relatively easy to route the ductwork, and also giving you a very short run of duct, which has some advantages (minimal flow resistance, easy routing and installation).

There are some potential disadvantages, however, of that approach. This approach virtually mandates the use of an internal blower (the electric "fan" that blows the effluent out of the hood_--so that the motor that powers the fan will actually be inside the actual hood. This is the most common arrangement, but it has significant disadvantages compared to a "remote blower"--a fan unit that is mounted at a distance, typically either in the attic, or on the roof. There is a much longer run of duct, which can be a challenge, but the big advantage is that the noise of the electric blower is moved out of your kitchen and the result is highly efficient ventilation and very minimal noise levels.

Post this to the Appliance Forum where lots of ventilation-obsessed folks hang out, and give more specifics, and you'll get lots of good advice.

"This approach virtually mandates the use of an internal blower... "

No it does not.

You can put a remote blower directly on the side of the house at the vent exit.

The do not have to be on a roof.