As it has been frigid where I live, my edge for the last three days has been making a buzzing or grinding noise (sounds like a vacuum cleaner) when I crank it up cold. The noise seems to come from the transmission. Especially if I turn the steering wheel left or right. Once the vehicle warms up, the buzzing/grinding noise stops.
that sounds like power steering , not transmission
Especially if I turn the steering wheel left or right
Check/top off the power steering fluid. While the hood's up, have a 'helper' turn the steering wheel back and forth as the engine is idling. The power steering pump (or anything on the belt's drive line) should sound only slightly louder when they turn the steering back and forth, left and right.
PS systems need fluid changes too. Dirty fluid can ruin a pump or a rack. Either on starts going bad and a noisy one can make a sound that resonates throughout the drive terrain.