My truck just started doing the same thing wile my wife drives it to work, but I haven't had a chance to address it yet. It has been well below zero day, and night, here.
From your description, I would say check your transmission fluid level. When the level gets low, the transmission hangs up while trying to downshift as you stop or slow down. The sudden load on the engine can cause it to stall and die, especially when you add the turning of a power steering pump, and the fan on high/brake lights pulling from the alternator all at the same time.
Something else you might try, if the level is fine, is put your truck in neutral (with the parking brake set) while warming it up, so the trans fluid is circulating the whole time, causing it to warm up while it's parked.
Last week, when my overdrive wouldn't work, I discovered that our trucks will not allow overdrive below a certain temperature, due to the trans fluid being capable of freezing.
I had to cover my trans cooler with cardboard and warm the truck up in neutral to get the fluid to a temp high enough to allow overdrive. Depending on how cold it is where you are, the thickness/temp of your trans fluid may be causing the same hang-up in the trans that low fluid would, which is why you only see the problem on your way to work, and not on your way home (after the temp has warmed up).
Before I covered my trans cooler and after driving several miles without my overdrive working, I tried to put the trans in neutral as I pulled over. The trans hung up so bad coming out of drive and into neutral, that it jarred the truck and killed the engine immediately. I went home, covered the cooler and let it run in neutral for a few minutes. It stopped hanging up immediately and overdrive worked right away too.
I will be doing the same things, as well as cleaning the battery terminals to assure a solid ground to the battery. If you follow along, I bet your problem will stop. I will keep you posted on my progress as well.