No hot water after teeing to outside spigot
In the normal faucets and showers in your house, the valves governing the flow of hot and cold water are before the mixing of the two. Even when these valves are wide open, the water pressure will decrease across these valves, so that where the water mixes is at a substantially lower pressure than in the source pipes. This prevents the mixed water from pushing back up the cold/hot water lines.

Here, though, your valve is after the mixing, so there's no pressure differential keeping water from backflowing. Depending on your pipe routing, the altitude change (hot water rises), and whatever's in the middle, you could get all hot, all cold, or some mixture in between. Generally not what you want.