What can I wear in the cold weather to be able to bike to work (where I don't have a shower)
The general consensus I've seen is that you should expect to be cold for the first twenty minutes of cycling in the winter. If you're dressed warmly enough that you're not cold for the first twenty minutes, you'll swelter.

If your ride is under twenty minutes (this is just ballpark), you can simply dress warmly and remove clothes once you arrive at work. However, I suspect your ride is around twenty minutes long (given your description of a few miles). This gives you the unfortunate choice of 1) be warm initially but sweat towards the end of the ride, or 2) be cold initially but reach a comfort temperature right as you arrive at work.

I'm not sure there's a good solution if your ride happens to be right around this long. You might try dressing lightly enough that you're comfortable by the time you reach work, but try to get your temperature up before leaving by sitting next to a fire or a heater vent.