There could be a bad wheel bearing or worn front end components. Check the tie rod ends and ball joints for wear.
Warped rotors
You need the front rotors machined or replaced.
Does the steering wheel shake worse when you step on the brakes? If braking does not cause the steering wheel shaking you probably just have an out of balance wheel, a bent rim or a faulty tire.
if it shakes while your braking your front roters could be warped or if it shakes while your driving try balancing the tires at a tire shop.
Your AC should have NOTHING to do with your barking system, as it is not tied into the vacuum of the engine. If your wheel shakes under braking, then you need to replace your rotors and pads.
Warped brake rotors.
check your tires for a belt seperation. check steering stabilizer shock if equipt. if braking, check for warped rotors.
Warped brake rotor. Have the rotors removed and trued or replaced. Replace the brake pads at the same time.
It's PROBABLY warped disk brake rotors. Brake rotors will warp when overheated and if you go downhill very often, they've probably overheated. Replace the rotors with a high quality product and they'll last longer.
the brake rotors are warped. resurface or replace rotors. if the vehicle shakes without applying the brakes, check tire balance.
Probably i would go for wheel balance and maybe check your wheel bearings rotors will not make it shake because of speed
Most likely warped rotors