2005 Tundra SR5 TRD Double Cab 4x4
I have that same transmission cooler on mine. I live in Utah, and our mountains get cold. I'd reconnect it. I'd also run a grille blanket for the extreme cold temps. Also, doing a drain and fill on your radiator before winter would be a good idea. I did mine a few months ago. You want fresh fluid in your radiator yearly to make sure it warms and cools your engine properly.