Well yes, unfortunately hydraulics are a bit pricey (which in part explains the cost of some of the commercial offerings) - which would probably rule them out. But they have certain advantages that are hard to replicate with other methods.
You'll find that electric winches are geared down to match the high-speed low-torque motor to the low-speed high-torque requirement. But in selecting the winch, you need to calculate the required line pull, speed required, and amount of rope to be would in - and select accordingly. There's probably an iterative process here - calculate the values you think you need, look at the spec sheets, then see if you can revise the layout (eg switching from single line to double line pull to suit a higher speed, lower pull winch) to suit what's available.
A drive for an up-over-door won't work. They are designed to take the counterbalanced load of certain types of door - no chance of them working one of these.
Be aware that the specs for a winch are not simple. You will see two values quoted (line speed & pull capacity) but these are only two from a selection of numbers ! Typically the suppliers will quote "first layer" values - ie what happens when you are winding the first layer onto the drum. When the first layer is full, the effective diameter of the drum increases because you are now winding on top of the first layer of cable - so speed increases and pull decreases. Repeat for second layer and so on. All assuming the cable lays up neatly which it often doesn't.
On that last bit - the capacity of the drum is markedly different for well laid up and random winding of the cable. Forcing a good layup of the cable is hard and often need an active cable guide to position the wire as it's wound up. If the line pull is dead straight then it may do it on it's own ...
For an AC motor I suspect the speed isn't greatly affected by load, but for the DC winches I'm more familiar with there is also a huge variation of speed with load. Ie they run "quite fast" with no load, but as the slack is taken up, the speed drops off considerably. For these, line speed is often quoted under no load - which isn't very useful.
Obviously, the figures you get will depend on how good the seller is. If it's an outfit that prides itself on support etc, then you'll get full details (and possibly graphs). If it's one that just wants to shift boxes, you just get the two numbers quoted (which will be the best ones) and it's up to you to figure out the rest.
But with a winch, there is still the issue of how to deal with a cable failure.
I suppose you could rig up some form of damper (one each side) ? Cable (separate from winch) from bottom of door, over pulley, down to plunger set in a tube. Plunger is weighted (could form the counterweight already mentioned by the OP) to make it sink in some oil or water, had a non-return valve to let it sink (could be simply a disk sat on top of the plunger which has holes in it), but when the door is lowering, the oil or water must go through a smaller orifice and will thus control the speed of a runaway door.
Or some form of mechanical safety brake as previously described.
