Biking gloves with finger protection
Usually when you fall on asphalt, fingerless gloves do cover the area of impact. 

Lots of manufacturers do make cycling gloves which are full fingered, such as the Giro Bravo shown below:

 

You may feel more comfortable with this, but your hands will get a bit warmer and having open fingers helps making some adjustments a bit nicer. 

Depending on how cold your winter is, combining a thin running glove with a standard fingerless cycling glove may be adequate and provide enough protection as well. I often use this when its a bit chilly (say around 30F). When it gets into the 10s or 20s, I might double up a thin running glove with something like a Underarmour Coldgear glove -- not too thick, but layers are key for cold. 

However, depending on winter riding you may want something like a lobster claw like the following Pearl Izumi's (possibly combined with a thin running glove - great in under -10F ish weather): 



Or if you're in the crazy cold, pogies:



(from Icebike's protecting your hands page)