I cover up everything, and agree it's cooler than uncovered when directly in the sun. The experience is mixed when in the shade, depending on humidity and material of cover. Some fabrics are cooling and/or temperature regulating. Merino wool is surprisingly comfortable in the heat and sun, as is mulberry silk satin with air vents.
On my feet I either wear minimal shoes or functional cowboy boots (not the dress ones that have pointy toes, these are work boots with wide square toes), depending on if I'm going to be in areas there might be cactus spines on the ground, or dry tumbleweeds, other dry spiky things, and all.
On my legs I wear denim. I love the tan denim, but it's usually too heavy duty for me to actually work in (especially in summer), so I tend to just wear blue jeans. Lately I've been wearing stretch denim jeans a couple sizes larger than I am so they fit without stretching when I'm standing. The stretch is nice when squatting and lunging, etc. while working. My legs hurt in the sun without being covered--the sun is so strong. I'm so much more comfortable when in long pants if I'm going to be actually in the sun. My husband doesn't have the skin issues I have and often wears shorts and goes without a shirt, but he always has more issues with the heat than me too. I think that's part of the reason why.
I prefer natural fibers, however after the 20th skin cancer spot cut out of me (18 on my face) I decided to be more open to other possibilities for my upper body. My skin, especially my face, is super sensitive to anything on it (allergies, rosacea, etc), so sunscreens just aren't an option (and I've tried them all). Also it's sensitive to physical irritation so sunglasses, hat bands, sun gaitors all have turned out to be a problem (all of those 20 spots were places where something had rubbed on my skin fairly regularly). I was enjoying merino wool for some things for a while, but that became too rough for my skin if worn daily.
So when it comes to sun exposure I've found over time that I need to use those UPF 50+ fabrics (usually polyester mostly) that have physical sun blocking properties (not treatments to them, so doesn't come off on me or wash out). The bonus of those is they are also often actually quite temperature regulating, so I am quite cool in them. It was 124 degrees Fahrenheit yesterday and I was totally covered up and fine.
Since I can't wear hats so much anymore (general irritation + extra from the newest Mohs surgical scar running from between my eyebrows up to my hairline), I have hoodies that have brims instead. I often wear a cotton tank top under the hoodie. The hoodies have long sleeves with thumbholes so that they stay down over my hands. They're great for when I'll be bending over a lot and/or in the wind for cover. They zip up to over my nose, just under my eyes, which is great except my nose was not happy with the zipper there... so I found some full face masks made of mulberry silk satin for my face and zip to my chin.
In the past I tried hats with things hanging over my face from the brims with the idea that I'd be able to breathe better, but it didn't really pan out that way and I couldn't see when I looked down because it would hang in my line of sight unless I held it back which is not practical. I also tried a face shield thing that is 50+ UPF, but it ended up making a greenhouse effect and got too hot, even though it sat away from my face I couldn't breathe so well in it, and it was so heavy that the headband it was mounted on would have to squeeze my head too much for comfort.
This mask is great. It has soft adjustable ear loops like the masks people wear to avoid airborne things, but it's different than that. It covers my entire face with the exception of just my eyes and the bridge of my nose between my eyes. It has a vent at the nose area which only opens when I breathe harder so my skin stays covered and I breathe freely. It's double thickness so that when I sweat on the inner layer the outer layer stays dry, which helps maintain the UPF tightly woven silk naturally has when dry. It's soft and flexible, fits loosely so it's not an issue. Then I wear UV glasses over the mask that are wide enough at the bridge of my nose to cover that too. The mask allows me to wear sunglasses without all the skin issues because my face has been great with the silk and the plastic of the glasses frame never touches my skin.
I have thick soft leather gloves to wear as needed depending on the task at hand. I put the gloves right over the sleeves with my thumbs still through the thumbholes and it keeps the sleeves down as I reach and do things.
So, yeah, not exactly trendy ... but it may be starting a trend. I've gotten a lot of compliments on it with people asking where they can get the hoodies in particular when I'm in town. The one I wear to town is a little more stylish than the one I wear for outdoor work. Both are UPF 50+, loose, and temperature regulating. I just have to unzip while taking off the hood, pull the mask and sunglasses off, and I'm good for being indoors. I have the glasses on strings that are attached to my hoodie instead of just around my neck. That serves 2 purposes: keeps my neck free, and counterbalances the brim on the hoodie which would pull the front up otherwise. So the only thing I need to stash when I go indoors is the mask, which is quite simple to do. It's funny because I'm taking off my mask when I go inside and putting it on when I go outside, where people wearing masks for airborne things are putting their masks on as they go inside--opposite!
I ordered a legionnaire's type of hat (has a brim and loose cloth to cover sides and back of head.. but this isn't like a baseball cap brim, it's wider and flat-ish) a few sizes too large for me so that I could try wear it over my silk mask, maybe that will be another option too. Whatever the case, I cover everything now.