What is recommended before you start exploring off pavement? (see below)
Outfit your vehicle with terrain appropriate tires. A "severe snow rated all-terrain" tire makes a good all-around tire choice. You may need to downsize your vehicles wheel to open up more all-terrain tire selection. Here's a link to the tire size calculator. This will help you source out what tires you need.
Busting your oil pan, transmission or differential is not only expensive, it can leave you stranded in the middle of no where. Protect yourself and your investment by spending a few hundred dollars on skid plates.
Here are popular skid plate manufacturer's:
-LP Adventure (CRV only)
Depending on the terrain, you'll need to adjust your tire pressure accordingly. In soft sand and deep snow, most crossovers should be at 15 PSI. For Rocky and loose terrain, you'll want to be at around 20-25 PSI. Whatever the case may be, you'll need the means to air back up. ***I'll link my recommended tire inflators in the "recovery gear" tab.***
Blowing out a tire on a trail is a very REAL possibility, and the little donut spare isn't made to handle rougher terrain. You safest bet is to run a full size spare tire!
Finding a place to mount a full size spare can be a little challenging. In my old 2015 Subaru Forester XT, I built a wooden frame to raise the cargo floor (pictured). This allowed a full size spare to fit. A popular option is to place a full size spare on top of a cargo basket but the only problem is it will greatly increase wind drag and will drop MPG's, we are talking anywhere between 4-9 MPG. You can always carry one in your trunk area, place one in a roof cargo carrier, or purchase a rear hitch tire carrier. JUST, DON'T LEAVE HOME WITHOUT A FULL SIZE SPARE.