Okay, bare with me, I'm recovering from a flu that's kept me home since Friday, so this idea may...okay isn't the best. You have an umbrella with a heater in it. Then you have a large see through plastic that goes from the bottom of the umbrella to your feet (I've already seen this somewhere). This plastic keeps you inside the umbrella and thus keeps the warmth in.
So how do you power it? Let's think like an environmentalist and go with Solar. But umbrella's only come out in the cold so no sun. We could use wind power, but then a large blade on top of an umbrella could be dangerous. That count's out the green approach.
What about Nuclear? But then a nuclear powered umbrella sounds more like a plot device in an action movie (now there's an idea!). We need an energy device that can power a heater for a half hour period (say) and is rechargeable. Are batteries powerful enough for that now days? They can run computers for several hours so they should be able to run my umbrella. You'd put the battery in the handle
The problem with this device (among many problems) would be weight. But maybe one day we'll all be holding one of my Heatbrella's (hey, I have a flu!)