Just purchased my first crossbow and was wondering if any tips on protecting it in the rain.

don't really think rain would do to much damage. Just like a gun or anything else you care for, if its out in the rain or something like drop it in puddle etc etc..just bring it in that night and give er a quick wipe down and some heat to dry whatever out. if you really wanted to put something on the crossbow for the rain make sure your string is always waxed real good and just put some wd-40 on a rag and wipe some parts down like the cams or the scope and mount etc.

make sure you wax the string
I won't go out in the rainy day.

Nad ashort of totally covering which makes zero sense.

Make sure that the rail is well lubed, the serving area is waxed properly. If yours is a compound X-Bow, make sure that wheel bearings are properly lubricated.

When you return to the camp, dry it off good ASAP. If possible use a hair blow drier (on low). Re-lube and re-wax and you are good to go for the next hunt. The modern strings and cables are not as moisture sensitive as the "old stuff" I have used way back when. But I would check the POI as soon as practical.

I dry the bow my air compressor and a hair dryer on low. Then lube with a rust inhibiter.

Use eezox on all metal parts that need protecting including squirting some in the trigger group.
http://www.6mmbr.com/corrosiontest.html

I always dry my cb well after hunting in the rain. Also keep your string/serving waxed up good & keep the trigger mech lubed. Most moisture displacing types work fine. I usually use WD-40 since I always have a can laying around.

Being retired, I don't do rain either.

I don't bow hunt in the in the rain it seems a little unethical to me hard to blood trail a deer when the rain is washing the blood away. If you get on them too soon they can really go a long way when jumped and wounded. Best to wait it out and better for your equipment.