I imagine it got much colder and wetter in the medieval period.

You might actually be surprised. The 'Medieval Warm Period' was a weather phenomenon that peaked between 900 and 1100 in Europe, but really dragged on until the 1300s that saw warm temperatures and mild winters only surpassed until the 20th Century. Indeed, Mann's 2009 study suggests that, while global temperatures are warmer today, areas of the North Atlantic, Nothern Europe and North America were actually warmer than the 20th Century. On the other hand, areas of Eastern Europe and Central Asia were far colder than today. There are a few theories as to why this might be, from solar flair activity, to a lack of global volcanic activity, to wind patterns etc.

Still, it did, indeed still get cold. As you suggested, the most basic way to deal with this was to wear layers. The majority of medieval English clothing was from wool, which is known for its excellent thermo-regulatory qualities. Medieval clothing may have consisted of a thicker tunic, the adoption of trousers or leg wraps, and the wearing of a cloak. While many animals were slaughtered at the start of winter to provide preserved meat, those that were not were often moved to winter pasture. For those farmers who lived in long-houses, as can still be seen in Dartmoor, this likely involved moving the animal inside the house, although inside a 'barn' area rather than just loose in the living quarters. While conditions may have been a little crowded and smelly, they would at least have been warm.

There is always more to be said, but you may be interested in my answer to It's a cold winter day in 14th century England. What am I, a peasant, wearing?