I've been told by somewhat knowledgable people that drop bars aren't suitable for winter cycling in snow and ice. Is there any validity to this? If so, why, and which style of handle bar would be preferable?
Drop bars in of themselves are fine for winter riding. However, there are some peripheral issues involved. Your average flat bars will offer a bit more control in slippery conditions because flat bars are much, much wider than drop bars. A bike equipped with drop bars may not be the best bike for winter riding. But properly configured and sized drops can be excellent for winter riding.
Handlebar Width: Drop bars tend to be narrower than flat bars. You can mitigate this by getting wider drop bars; the ones meant for touring are great for winter riding.
Keep in mind that handlebar sizing isn't an exact science, but you generally want them to be as wide as your shoulders. A lot of road bikes won't have anything approaching this kind of width. (Also, there aren't that many wide, stocky roadies.)
Tires: Road bikes--which is where you usually see drop bars--often won't allow for the fitting of appropriate tires for riding on snow and ice. Not the fault of the drop bars!
Personal experience here, but I do not see any reason why drop handlebars wouldn't be suitable for winter riding. I have ridden extensively the past two winters with drop handlebars in ice and snow (Madison, WI). I personally find that in rougher and slippery conditions, I prefer riding with my hands in the drop position. It tends to give me better control while both giving me better access to the brakes and lowering my center of gravity a bit.
Despite snow and ice not traditionally considered commuting conditions, many choose to continue biking through the winter months. There are some good resources online with the best compilation I've seen being Chicago Bike Winter site..
One caveat I will make is that bikes that traditionally have drop handlebars aren't viewed as being optimal winter bikes due to typically having thinner road-style tires. Perhaps that is what the experienced cyclist was referring to.
Besides considering leverage as the only advantage of bicycling in icy and snowy temperatures, I would also consider the aspect of familiarity. My first few rides in icy/snowy conditions were quite nerve-wracking: constantly sliding right off the shoulder into the chocolate mousse or the ditch. I soon learned to avoid the treachery of the road shoulder and ride in the plowed area with the most asphalt exposed. One of the things that I felt good about was that I knew my bicycle well, and I wasn't making flustered or nervous mistakes with hand placement.
So, I would recommend focusing on keeping your hands and feet warm during the ride so that you are not impacting your ability to react or distracted by your extremeties. If it takes ziplock pogies and hand-warmers, or full-on BarMitts and Lake MXZs for your feet, being relaxed and perceptive to your conditions will make your ride safer than changing your ergonomics at the last minute.
And if you do ride in icy conditions and don't have studded tires, I would recommend those, too.