Disclaimer: Despite a comment I made earlier about how I too would like to hear about ways to test for hypothermia, I should stress that relying on this could be potentially dangerous and should be a last line of defense, not first. That is, always assume that you could be even if your test is negative, instead of assuming that you are not until it is positive.
1) Bring a watch, and estimate ahead of time how long certain activities should take. Time yourself doing them, and if it takes too long just assume you are compromised.
2) Bring a radio, and periodically (often) check in, preferably with the same person each time. Let them know ahead of time that they must tell you if they feel like you are reacting slower, or if you seem confused or otherwise weird. Cell phones can work if you are guaranteed good coverage.
I once noticed, because of a nearby clock, that it was taking way longer to do things than it should have. It was taking 10-20 minutes to do something that should have taken 1-2 minutes. I immediately abandoned what I was doing and tried to remedy the situation that was causing my decline. I might not have noticed if it weren't for my time keeping.
That said, the above situation was not hypothermia, but it was a different situation that can have a few similar symptoms, such as confusion, slowness and loss of time. Still, it makes me wonder if a watch could be a useful tool (again, last-line defense) for noticing some mental effects of hypothermia. Estimate ahead of time how long it should take to do certain activities, and time yourself. If it takes you 10 minutes to get out your pot and fill it with snow or water when it should not have, then immediately abandon your quest and seek help.
So the advise: Use a watch and keep track of the timing for your activities.
Since the above was not hypothermia, I was not going to post it as an answer. But I just realized I have another anecdote that is more closely related to hypothermia...
This next one is a negative, a warning that you might not detect it, rather than a positive.
I have recently started driving with my windows down and my arm outside the window while it rains. I have realized it's actually kind of nice to feel the wind and the rain. The rain stings at high speed when driving on the highway, but all along the rainy drive, it felt good, even invigorating, and I did not suspect any problems.
However, the last two times I did this, I did not notice until after, once I was done with the drive and sitting in a building trying to do other activities, that my arm and hand that was exposed to the wind and rain was not performing as well. When manipulating something with both hands, the one was not doing as well as the other. Or when trying to open a jar or bottle, I could not get the cap off using that hand unless the cap was already loose. When I touched the bad arm/hand with my good one, it felt cold to the touch of the good hand even though it felt fine by itself.
My situation was not dire, but it was still concerning.
Let's transfer this over to a case that is exactly in line with your question...
Instead of just the one arm exposed to rain and high winds, still having a good arm to test it against, what if I were instead standing out in a hurricane or blizzard such that my entire body was subjected to this? My entire body could get cold and not work well without me even noticing, just like my arm, but I would not have a known good part for comparison if I was by myself.
That is scary. Be warned, and be careful.
Back to the time keeping I mentioned above, I have read about high altitude mountaineers bringing lists of simple math problems and timing how long it takes them to solve the list of problems. In fact, I recently read about a few guys who decided not to do a climb they were about to do, because it took them twice as long as it normally took them to do a bunch of simple subtractions.
Your best bet is going to be not going solo. But if you insist on being solo and still want some of the benefits of having someone to help judge you, perhaps you could bring a radio and periodically talk to someone, preferably the same people each time you check in, and they can tell you if you sound weird, slow, or confused. Make sure they understand their job before you even start your journey and check-ins.
The radio idea also has the benefit that you can keep in touch with people and it can provide a morale boost. Obviously, if the area has excellent cell phone coverage then a phone call can serve the same purpose.