I DIY'd a terrarium for my gerbils and found the perfect material to use for the lid- a fireplace gate from the thrift shop ($5!!). The only issue is that I just need one of the doors and I can't get them separated from the frame.
Use of angle grinder, but with a thin cutting disc will be the best, but watch there are no windows, or any other glass in line of the sparks created. Once one hinge is off, lift off the opposing one, for better access.
A Dremel may get in closer and more tidily, with the correct attachment. Otherwise it's down to junior hacksaw (weld is usually quite tough to saw through) if you have an hour or two to spare, and then you'll still need to grind or file the rough remains.
Personally, I'd get the oxy-acetylene out, and very carefully unweld the hinge, but not many will have that luxury!