It will depend upon the terms of your policy if damages sustained while off roading will be covered by your "full coverage" auto insurance or not.

If off roading in your truck is allowable per your policy then the damages would be covered under your physical damages of collision and comprehensive. It would depend on how the tire and suspension were damaged as to which coverage you would place a claim.You can read through your policy as well as contact your insurance agent and explain your situation to determine if the damages will be covered by your policy.

You will need to make sure that your insurance policy does not have an exclusion against taking your truck off road and for damages done when doing so. Some policies may have an exclusion specifically regarding this, just as some have exclusions about taking sports cars on a race track.

If the damages will be covered then place your claim through your physical damages portion of your policy for the claims adjuster to decide if this will be a collision or comprehensive claim. Remember that you will be required to pay the deductible associated with this part of your auto insurance policy.

If your insurance company does not cover taking your truck off roading then you may need to find specialty coverage that will cover you for future off roading adventures.