Nope. Chances are you need to shut the water off to the spigot and bleed the lines dry to prevent pipes bursting. Store hose in garage, barn, shed, whatever you have.
You can cover the hose with the tarp but make sure you drain all the water out of the hose. I just drain my hoses and leave them hanging on the hose reel. Been doing that for years without any problems.
Just make sure you unscrew the water hose from the water pipe connection. The water will freeze inside the hose and burst. 🙃
check out my post all about your outdoor faucet in freezing temperatures. https://karupp-did.net/winter-freeze-ease/. This may help figure out what to do so your outdoor hose spicket doesn't burst.
I live in zone 8. When freezing weather is expected I disconnect my hoses and lay them on a slope to drain fully. It doesn't get cold enough here to damage the hoses, so I don't need to store them. In colder areas the hoses might get stiff enough to crack if stepped on, so ask your friends and neighbors how they do winter prep.
I think you should be sure your hose has no water in it that can freeze and burst your hose. Here are some tips for care of hoses in winter. How to Prepare an Outside Hose for Freezing Temperatures
No- you have to actually disconnect the hose, and drain it. Move it about to get all the water out. Turn the outside water off. Then if you have no where in the house to bring the hose, wrap it in the tarp, but better to bring it inside.