Impact screwdriver, you can purchase a cheap set that will probably last a lifetime . Or take a screwdriver and tap the end with a hammer while twisting the driver to loosen. I actually do not like tapping a screwdriver because it's too easy to ruin it.

I would start with a center punch and a hammer to turn the screw, if that did not work, I would use an easy out.

Clean the old paint out the slots, and possibly deepen the slots a bit with a hack saw blade. Cut around the outer perimeter of each screw head to break the paint bond between the hinge and the screw. Rap all the way around the perimeters of the screw heads with a pin punch and hammer to further loosen things. Then use an impact driver.

If that doesn't work, you may be able to cut the hinge off in pieces with a Dremel tool, and then remove the screws with a Vise-Grip.

Good advice. I would like to add, sometimes I will try and tighten the screw too. Sometimes it cracks it free.

Clean the paint off and heat the metal up with a big soldering iron. Almost always frees them up, it's a trick used a lot in non-destructively dismantling antique equipment with screws frozen in place. Most other methods make a mess of the screw, the surrounding wood, or both.

Clean off the paint and clean the slot. Use a screwdriver that fits the slot, the wrong size blade can ruin the slot. Most of the force holding the screw is between the metal parts. Several tips so far are good. Try the easiest ones first.

Simply smacking the hinge with a smooth faced hammer can work. The soldering iron works, but it usually has to be a large soldering iron, the pistol grip electric ones do not create enough heat.

I'm a big fan of impact screwdrivers, but in this case, that would be my next to last choice.

Last choice is drilling out the screw.

I use a dremel tool with a cutoff disc to deepen the slot.

Thank you all so much for the advice. Had to drop everything and go deal with a kidney stone attack (someone else's). Will give the shutter another shot tomorrow.

My vote is to clean out the slot or cut it deeper with a dremel and bang a good tight-fit screwdriver into the slot.

Multitool the slots deeper with a narrow blade (a dremel may work also) and then if it still doesn't budge once you have something to work with you might need an impact driver to get it loose. If all else fails you can drill off the heads. 3/8" drill bit might work. Once you get the heads and hinge off, you can grab onto the screw with a vicegrip and turn the screw out.

I got them out! I cleaned with mineral spirits, then used an exacto knife to scrape the perimeter of the screw heads and got some gunk out of the screw slots. I used a correct sized screwdriver and they came out pretty easily. Thanks again!

That's a satisfying feeling :-)