Well, even in system you are limited by your engines, so cyro would still be needed there.
Depends on the engines and how far you're going. And on how much cryo costs versus supplies, if the company cares about the boredom spent by their employees in space (and/or if the employees get paid en route if the're awake), et cetera. However, time spent travelling wouldn't exceed a year or two from Earth to the asteroid belt--we can currently get to the Belt in several months, IIRC, and there would be advances in space travel before asteroid mining was practical. Lunar mining would probably come first and, of course, would have no need for cryo.