plsander once bubbled...
They say the only stupid question is the unasked one... 
I know that most underwater lights should not be used above surface due to the need for the water to cool the bulb.
Does the same apply for underwater strobes?
Basically, No.
First, if you pragmatically look at a strobe and its flash tube design, you'll find that they're dry (wires suspended in an inert atmosphere within a glass tube which is also isolated via suspention in air inside the housing: there's no water nearby for the heat to easily get conducted to. A long, difficult conduction path is functionally thermal insulation, and not an intended system cooling path.
Looking further, beause all strobes dump their power in a few milliseconds, there is a discrete time lag between the generation of the heat and its dissipation (via water or air), which means that the net result is that it must be generally resistant to the "instant" temperatures generated by a single flash. I've not looked specifically into exactly how strobes do their thermal management, but looking at the above insulation design and so forth, IMO, much of the dissipation is probably by blackbody radiation, and not conduction or convection through a heat sink.
Heat generated by repetitive flashes might be a concern, but for consumer-oriented strobes, I think its pretty remote: our design objective is for a waterproof and portable device, so they're driven off of a smallish battery pack. As such, our strobe recycle times are on the order of 2-15 seconds (depending on the product's battery and capacitor designs, and battery pack condition), which gives us a lot of "power off" dwell time for cooling. The net result here is that we don't have the continuous runtime like we have with flashlights, so even though we have a really strong peak, we really don't have that much _average_ power.
Could a YS90DX (or YS25DX) be used on shore with the camera?
Sure, although I'd refrain from using it in the desert on a 120F day...but I'd also refrain from using it UW if the water temperature were 120F too. I don't have S&S strobes, but the brands that I have had/used haven't had any particular problem with casual use on land, other than it can be pretty darn hefty to hold the camera
-hh
