Welcome to the forum.
Your velocities are within reason for a 20" barrel. My M1A (22" barrel) always shoots in the 2550 fps range with typical match ammo. Figure the .308 loses about 20-30 fps per inch of barrel in that length range, though this varies with the charge weight.
The velocities you see published at Hodgdon's site
(or for commercial ammo) are for the SAAMI standard
length pressure/velocity test barrel. It is 24" ±0.010" long and has a chamber machined to within half a thousandth of an inch of minimum chamber diameters. That is done because a minimum chamber produces the highest pressures for a load, which is the worst case for the ammunition manufacturer. But with that highest pressure comes the highest velocities, and since most production rifles don't have the tight chamber or the exact same bore dimensions (also held to tight tolerance) they don't usually get as high a velocity even if they do have a 24" barrel.
At the Hodgdon site you will see a button that says "print". Only if you press that do you get a preview screen that includes the barrel length, case used, and primer used.
Most chronographs are made using consumer grade components. These are typically not rated below 0°C (32°F) so I would not be 100% sanguine about the validity of the measurements taken at 20°F unless the instrument instructions say specifically that it works OK that cold. Very often part of the problem is batteries that can't put out adequate current in the cold, either, so a lithium type is then best to use.
Also note that velocities measured to SAAMI standard have the midpoint between the screens at 15 feet from the muzzle. I usually use that distance for a comparison and also because, despite what the instructions say, you occasionally get muzzle blast effects from rifle loads that mess with readings at shorter distances. 10 feet works most of the time and is fine for handgun rounds, but with rifles I don't quite trust it. One fellow with a .338 Lapua Magnum reported having to go to 18 feet before his readings settled down.
One other thing about the chronograph, particularly one with short screen spacing (1 foot) is that it's easy to shoot a the bullet through it at an angle, which can lower the readings by giving the bullet a slightly longer path between the screens. I find the best way to handle this is with a laser bore sighter. When I set up the chronograph, I put a yellow plastic empty chamber indicator (ECI) flag in my chamber and then put the laser in the muzzle and prop the gun up on the bags so the sight stays on the target. I then go out 15 feet and fiddle with the chronograph stand until I see that laser light in the middle of each screen when I hold my palm there. This saves a lot of walking back and forth. When you return to the rifle you get to see exactly where the sights should be looking (above the center of the screens a little). And one more thing. The yellow ECI flag has the words "Remove Laser
" on it in black Magic Marker. I remove the bore sighter first, then the flag, always in that order.