Long term damage of phone being in extreme cold?

There's really no way of knowing without disassembly. Cold temperatures aren't necessarily so bad that by itself it damages the electronics in an iPhone unless it's some kind of extreme thermal shock, like pouring ice water in a heated glass. The battery is going to be the weakest point. That's likely what the storage temperature limits are about. It's not good if the battery freezes. With operating temperature, being cold is actually quite good for the electronics, but not for batteries that lose performance when they get too cold.

iPhone 8 Plus - Technical Specifications

Environmental Requirements

Operating ambient temperature: 32° to 95° F (0° to 35° C)

Nonoperating temperature: −4° to 113° F (−20° to 45° C)

Relative humidity: 5% to 95% noncondensing

Operating altitude: tested up to 10,000 feet (3000 m)

It will have several liquid contact indicators (little adhesive devices that turn red when in contact with liquid water) where that's a sign to service personnel that it's been in contact with water. If any show signs of liquid contact it's pretty much ineligible for service from Apple or an AASP other than a complete replacement with exchange.

About the only thing I could think of that's DIY is to check the LCI inside the SIM card slot. This article shows the location.

Water and other liquid damage to iPhone or iPod isn't covered by warranty - Apple Support

The worst thing with rice is not just that it's ineffective, but that rice dust and water has about the consistency of dried glue once it's dry. Other than that, often the water resistance holds. Doesn't always, but just because we hear a lot of horror stories doesn't mean that there aren't also happy tales.

Keep an eye on it (especially the battery) and good luck.

None of your questions are "stupid." They actually make great sense in these types of situations. You appeared to have done just about anything possible to try to recover your iPhone (I would suggest not using rice or any desiccant in the future as it could potentially introduce other debris into the phone.)

At this point, unless you have your phone examined by an Apple technician, it would be impossible to guarantee that liquid did not enter the phone. As such, if available I would suggest that you make a Genius Bar appointment at your local Apple Store or Apple Authorized Service Provider to have them take a look and provide you with your options. Alternatively, if neither are nearby, you can contact Apple Support directly for assistance with this matter. To do so, simply select the "Get Support" link in the upper right-hand side of this forum's web page.