Personal liability follows you off the property
An accidental injury you cause while hunting is generally a personal liability claim, and your homeowners policy responds wherever it happened. That is genuinely broad cover, and the limit on it is usually whatever was offered at the original quote rather than anything chosen.
A firearms injury is a catastrophic claim
These are rare and they are severe. A single serious injury exceeds a standard liability limit comfortably, and the claim is made against the household. This is exactly the shape of loss an umbrella exists for.
Guiding or charging money changes everything
Taking payment to guide, outfit or host hunting turns it into a business pursuit, which personal policies exclude. The line is money, and crossing it casually is how an insured activity becomes an uninsured one.