Long ago, in a body quicker and more nimble, I went out one Sunday for a long run. I got exactly as far as the front porch before hitting the ground.
Clearly I wasn't still living in SoCal where a 'winter' run involved a long sleeve shirt. Bruised ribs weren't going to stop me from getting my run in, though, so I took off from my house in Moscow, ran across town and the University of Idaho campus.
I picked up the Chipman Trail at the edge of town and headed for Pullman. Hah! Nothing stops a determined runner.
Two more hard falls on the trail and I came to the stunning realization that I just wasn't that frickin' dedicated. I called my wife from the Chevrom in Pullman and she kindly fetched me from near-certain injury. As it was, it took a week for everything to heal.
Fortunately, nothing was broken. A friend of mine, Lance, wasn't as lucky and finished with a concussion on his run.
Running on ice is more than tricky - it can be downright hazardous. So, a couple of thoughts from a guy with memories of bruises.
First, decide if there might not be another way to get the run in. We runners are creatures of habit. If the long run is supposed to happen on Sunday morning at 7am, by golly, we're going to make it happen. Consider that at 1PM, the ice might have melted. Opt for changing your schedule instead of trusting to your luck.
If you do have to go at 7AM, try running in Yak Trax. I've never used them but friends that have say they work well in crappy conditions. All the sporting goods stores have them this time of year or you can snag them on Amazon.
The last, and least desirable option, is the treadmill. Given that 15 minutes feel interminable on the 'dreadmill' for me, all I can do is wish you good luck. I forget which US marathoner (from Alaska, I think, and female) did all her long run training for Boston on a treadmill about a decade ago. It can be done.
If all else fails, skip the run. Sacrilege! But a better option than breaking an ankle, a hip, or our noggin.
Good Luck, run gently, fall more gently if you happen to go down.