Yeah thats a bitch, same ting happened on my 2000 GC. It took a while to
figure out, dealer will tell you that it has to be cut down. What happens is
there is a safety lock mechanism on the winch. It locks the wheel up so that
if the cable rusts and breaks the tire won't fall out from underneath. It is
held up by a plastic rod which looks like large bolt. Go to the dealer and
have the parts guy show you ALL the views of the winch assembly, you can get
the spare down by spending a few hours underneath, prying and twisting at
the lock mechanism. Then clean up the road dirt and lube the heck out of the
cable and mechanism, preferably with a dry lube so it does not attract dirt
easily. I wish I could explain it better, but I did this last winter and
can't explain the exact procedure I used and its not in any manual or
Caravan book I saw. I was not willing to pay the 150$ the dealer wanted for
the part.

P.S.
Did you follow the procedure in the owners manual to drop the tire or did
you just start cranking. If you don't do it right you will never get the
tire down after cleaning up the lock mechanism anyhow. It is very specific
on how to do it and after cleaning mine worked fine.

regards

Had the same thing on my 99 T&C. Jack the rear of the vehicle up. Wind the
spare "up". Now put your jack under the spare to support it's weight. Than
"unwind it" now look up through the spare to the winch assy. You'll see a a
latch. at the back (toward rear of car). reach in with a long screw driver
and release it (move it towards rear of car). If you've uunwound the winch
prior to this point you should be able to move the plastic holder downwards.
Once you've done this you can now allow the tire to come down. Once the tire
is down and off the cable remove the jack assy. 5 or 6 bolts. Odds are
you'll see a piece of "wire" hanging or may have fallen out. You'll also
seea spring clip (again either laying on ground or look at the assy. itself.
It clips on the underside so when you unwind the unit it should pull the
aforementioned latch to release the tire. If you fiddle enough you should be
able to get it back into place. It is definitely rube goldberg. You could
just attacha wire to the latch and keep it over the tire so you can release
it manually or live dangerously and disable it all together. Or buy a new
winch.
Larry

cut the cable and by a new wench