Keep It Simple Superstar

The more basic your drivetrain is, the less it requires attention and maintenance.  For winter riding, you may want to consider a single speed set up.  Even the largest hills can be tackled with the proper selection of gearing.  An easy spinning gear ratio also has the benefit of allowing a higher cadence to help keep your body warm.  When the temperature really drops, wind chill becomes less of a factor at lower speeds.

This is your typical single speed drivetrain.

Notice the horizontal dropouts. Just slide the wheel back to keep the chain at the proper tension.

This bike was originally equipped with a geared deraileur system.  A single speed rear wheel was installed and I found what is called "the magic gear", meaning that a chain tensioner is not required.  The size of the front chain ring and rear cog just happen to work with the length of the chain.  If either one had even one less tooth, the chain would require some way to keep it tensioned to ensure it did not come off during rough riding conditions.

This bike was originally a geared bike but with this conversion, you can clearly see that a tensioner is being used in place of the deraileur.

This system has the benefit of using a much longer length of chain that allows the use of two front chainrings, making this bike essentially a two speed.  Notice in this photo that the chain is on the outer chainring and the tensioner's position has changed.  On this bike one gear ratio is used for trail work, the other gear is for road speed.

Winter riding on any of these setups requires that you only keep the chain clean and lubed.