This is a cross/multi- thread post.
There are a few factors I'd consider when airing down:
1. Experience level riding off-pavement
If you have little to no off-road/off-pavement riding experience, then most-likely the only times you've ever experienced losing traction was a moment of PANIC and TERROR which you never wanted to repeat. The DL is a top-heavy beast, more noticeable especially at slower speeds; if you're moving at any speed, there is very little time in between the front-tire starting to slide out and the entire bike going down.
Airing down the front tire, will give the motorcycle a much more PLANTED feeling, and won't "ping" the handle-bars around off minor rocks and bumps. For riders new to riding in low-traction situations, consider airing down the psi to "train", so you can get accustomed to the low traction handling without having to worry as much about the handle-bars being slammed around (sometimes rather violently).
I recently went off-pavement, taking my front Dunlop TR91 down to 20 psi (which was actually lower than I intended, maybe 25psi +/- better), getting back to the pavement with no punctures or bent-rims (the roads were pretty well maintained). I left the rear tire at street pressure (40 psi +/-).
More experienced riders who are used to low-traction conditions probably can do fine running street pressures on most well-maintained forest roads, since they know what to expect to feel in the steering when going over bumps and gravel. The pros of not needing to air-up afterwards, and not worrying about catching sharp rocks thru the tires, will out-weigh the benefits of having softer, easier, handling.
2. Difficulty and duration of road/terrain
Most well used/maintained fire-roads and backroads probably won't have too many big rocks and bumps that pose a serious threat to a tire w/ reduced pressure, especially if you are picking good lines and staying attentive. If you are going on a longer distance off-pavement adventure, with big rocks/slides, harsher bumps, higher-speeds, (usually for more seasoned riders), a low-psi tire will increase the chance of a trip-ending damaged tire or bent rim; (likely worse than a low-side that you can otherwise just pickup, brush off, and go at it again). Depending on your load, airing down (maybe down to around 30psi +/-) will dampen the steering a bit, and still keep the integrity of the tire to resist sharp edges and rim damage. It was said earlier, hitting a square-edged bump at high-speed can damage your rim REGARDLESS of tire pressure (lowering the pressure a bit can even help absorb the deflection in some situations).
If you are only going to be off-pavement for a short time (only a few miles) on easy well-maintained roads, it's probably not worth it to air down, then having to break out the air-pump once you get back to the main road. Just take it slow if you are getting used to the low-traction.
3. "Quality" and characteristics of your particular tires
I think most of the tires available for the DL are radial-belted type (someone correct me if I'm wrong), so at lower pressures they aren't as stiff, making them more susceptible to damage from sharp edges and rocks, especially the sidewalls. I imagine different tire brands/models will have slightly different optimal psi-ranges, anywhere from 20-30 psi; there probably isn't a magic one-psi-fits-all number, but if you were to ask me, I'd say 27 psi is good when going off-pavement under most conditions. Why 27? Just because I like that number a lot! And it seems like a good compromise of both.
Last bit of advice:
Throttle on AS YOU START your turn-in! If you are a new rider trying to get used to the low traction, take it slow, keep the bike upright, easy on the front brake, and use the throttle! Smoothly engaging it whenever things seem to get bad, you'll be amazed how the bike truly wants to keep going when it's under power (and how rider panic and abrupt braking/steering-inputs are what can disrupt this balance).
One of the fun things to do, once your confidence is built up a little bit, is seeing that turn come up and balance the "steer-in/turn-in/lean-over with the throttle rolling-on", giving almost a 'snowboard carving' like feeling as you plow through the corners. Grabbing "too much" throttle can be more exciting, but rarely will it slide the whole rear-tire out from under you unless you are in first gear over some really loose material. It can also result in a high-side if you suddenly regain traction, but if you are standing on the pegs with your weight forward, it's less likely.
Have fun out there!