Can the reel be removed for winter storage without removing the wall plate?
Yes,  The post-mounted hose reel can be removed from the axle/wall plate without removing the wall plate from the post.  Please see the steps below.
Disconnect your hose from the brass swivel.  (You will leave your hose wrapped up on the reel for storage.)
Unthread the brass swivel from the axle of the reel by loosening the silver retaining nut from the axle by turning it counter-clockwise.
Pull the swivel and about 6” of hose out the front side of the reel
Unthread the brass swivel from the inlet hose.
Slide the cam-lever brake off the axle.
Slide the hose reel off of the axle and take to your designated space for winter storage along with the swivel, brake, and inlet hose assembly.