Take the bike to the fire trail you want to ride.

Ride the bike on the trail.

If you slide more than you like, or if you get some flats; get beefier tires for that trail.

If you have no problem, then your sturdy Continentals are just fine for that particular dirt.

(Trek420 rode that same bike on those same tires on a dirt and gravel trail as part of a long and glorious test ride a couple years back. Don't recall her having a single complaint. She also rode off a curb or two. No problem. I have very similar Continentals that are only 23mm wide on one of my bikes, and they handle gravel and dirt fine.)

You won't know until you RIDE.

More riding, less worrying.