Also, they are wool with a low pile.

If you think of them as disposable, then leave them outside. If you prefer to think of them as investments for the ages, then have them cleaned by a professional and bring them inside. They likely already have insect issues if they have been out more than a day or two.

The rugs were made for nomads. Some existed on dirt floors. If they are out of the sun, not getting wet and are to be brought in for the winter, a month or two should not destroy them PROVIDED they are cleaned and taken care of. Insects will always be an issue if the rugs are outside.

You should decide if you only plan on using outside from here on in and only for a few years. They will absorb/retain liquid, are not UV-treated to prevent fading, and are not or mold and mildew resistant.

Most outdoor rugs are constructed with a backing material of either polypropylene or another synthetic fiber so they are resistant and will not deteriorate over time.

I, too, think they look fabulous outside, but I doubt that it's very good for them, and I personally think that you'd be making a big, horrible, awful, insane, bordering-on-evil mistake. Hand-knotted rugs are works of art and deserve much better. If you want something that looks similar, but in polypropylene, try Ikea's Valby Ruta. It won't last for long out in the elements either, but it's attractive, has a soft pile, doesn't appeal to moths, and is quite cheap. When you end up throwing it away, it can easily be replaced. I used to have one of them on my own patio, but it died a sad death (I love all rugs, even cheap ones). Since then, I've been sticking with Mad Mats. They have a couple that are in a "traditional" style, and while no one would mistake them for anything other than plastic, they withstand anything and look pretty awesome, imo.

You know if you love the rugs there keep them there,,
I,have hung onto oriental rugs for years ...no one else wants them in my family my motto is use them and enjoy them!!!
They were used in tents for years

I think there are a few things to remember, here. Hand knotted rugs like the ones you have are made of wool, and any insect or critter that likes to nibble on wool will nibble on them. Those rugs will most definitely fade in the sun, and faster than you'll imagine. And while its true that rugs were laid as floors in tents, the better and more valuable ones were woven for mosques and for fine houses, not for nomadic tents and yurts. All of them were in places with very little exposure to sunlight. So putting on the deck to me is a no-no. That said, the rug on the left is too far gone anyway so it might as well stay out, but I'd bring the one under the trunk back inside.

Thanks everyone!! So happy to get all your feedback. Would a polypropylene rug solve the critter/bug issue?

keep them inside

Poly will solve lots of issues. We have a very large customer poly rug running our entire patio, which includes under our dining set and into the conversation area. We've been in the house 5 years and I believe it was laid down a few years prior. We have some severe weather where we live in Canada and this rug remains outside all year and it's still looking good.

can you buy a product to reduce mold... for carpets outside?

I am a retired rug professional and love to use orientals everywhere. BUT, I would go for a polypropylene rug and use your original handwoven rugs indoors.