The vent is connected to the interior of the microwave---yes?

If so, that cold air will only intrude to the inside of the microwave---not a problem unless you leave the door open.

If the vent connect to the shell of the microwave, see if there is a way to seal the shell(case) exterior---contact the manufacturer of the microwave.

You're going to get cold air coming through the vent regardless of how you vent it, but if you use a quality exterior vent, it will be minimal. IMHO, it is always better to vent directly out the side exterior wall than to penetrate the roof.

"You're going to get cold air coming through the vent regardless of how you vent it"

I disagree with this statement. I used a spring-loaded backdraft damper in my duct, and have no such problem. Going straight through the wall, however, may make the duct run so short that there's no room for this extra piece of hardware.

What if I run the duct through the top of the mwrange hood and go 2 feet up and then out through the wall. This will put an elbow in the duct and may stop the cold from coming in. What do you think?

I'm not sure what you're imagining, but air can go around corners. The elbow won't do a thing except reduce the performance of your hood. You need to make it difficult for air to enter and continue through the pipe. The MW hood may have a built-in backdraft damper, which would be a good start. Look it over and see - is there a gasketed, spring-loaded flap on the back that is normally closed but that can be pushed open by the fan-driven air? Even if there is one, it would be good to supplement it with either an inline damper (Google "Fantech RSK6" to see what I mean) or an exterior hood with a gasketed, spring-loaded flap.

Here's a link-click on products,then household. It's a dryer vent that converts by use of a spring kit.

Here is a link that might be useful: energy saving vent

sorry,i gave you the wrong website.

Here is a link that might be useful: vent