Half-Ton Trailer Camping at Yosemite

Thanks for the extra info!  We were on the mad dash for sites this morning.  Tried to get one at Lower Pines which, in the end, we thought that would be better for us anyhow because it's right on the shuttle bus line.  That didn't matter because we got skunked.  After the 7am release sites were gone in a minute.  Our first second "the website is experiencing heavy traffic".  Our next refresh "Unavailable"... 🤦‍♂️  On the upside, we did get a spot at Hodgdon Meadow so I'm encouraged that you've gone up with your 24' Komfort, that would be very similar to our length.

My bad. I thought it was driving apprehension not equipment concerns. 
I’ll check but I’m almost certain those 10 speeds run around 200deg normal operating temp. My last 2 Chevy 10 speeds did (same trans). I’ll check the F150 I’m driving now. 
Keep the gears low, rpm’s up especially if the trans is building heat. And good trailer brakes. Wouldn’t bother me to pull that trailer with that truck up a mountain. 
If I showed you pics of 10klbs on a 4klb trailer behind a half ton Silverado with the factory weenie rear tires pumped up to 65 psi over Chinook, Cayuse, White, Snoqualmie, Blewett, or Stevens passes or pulling the grade out of Vantage either direction from the Columbia. Sometimes on hot summer days, you would have no worries about your trailer in Yosemite. 
Let er buck!

Quiet day, so I got a bit wordy:

GVWR of the trailer is 6000lb...If the truck has a 9000lb tow rating, you are well within the motor's capability.

 - transmission should have no problem. It's mated to more powerful engines.

 - The engine can put out the power, just watch the engine temps. On flat ground, you are likely running little if any turbo boost. If you keep the hammer down on a long grade, you are likely running a lot of boost the entire time and burning a lot of fuel. That creates a lot of heat in a small engine block. Probably won't be a problem as you aren't pushing the truck to it's limits. If you can feather the throttle or run in a lower gear, so it isn't running a lot of boost, that's good. Worst case if it starts getting hot, find a place to pull off and let her idle for a few minutes until temps come back down. Don't worry too much about speed, these are routes geared toward tourists watching the scenery.

A good way to check grades is download google earth (different from google maps) onto your laptop. Enter your route and then right click on the route. It will give you the option to show elevation profile. We've found it pretty accurate for determining how long and how steep the grades are.

For fun, I pulled up the routes to look:

 - Hodgodon Meadows: Out of Coulterville, you have a 3 mile 7% grade. Then a bunch of short up and downs. Then two separate 3 mile 6.0-6.5% grades. (ending elevation ~5000ft)

 - Mariposa to Bridal Veil: Starts with a 3 mile 6% grade, followed by a downhill 3 miles at about 7%. Probably the worst of it as it's on a twisty section but nothing crazy. Then a long modest grade mostly around 1% ending with a 9 mile climb ranging from 4-6%. (ending elevation ~4000ft)

Use the tow/haul and/or force it into a lower gear starting downhills. Start the downhills a bit slower than you would be comfortable with. If the speed starts getting a bit high for comfort, firm braking until you are slowed down and then release the brakes. Don't ride the brakes as this can cause them to overheat. By releasing them, the brakes have a chance to cool down.

All that said, you should be fine in terms of grades (I didn't check any length restrictions and it's been a few years since we were there).