Winter is a middle season, when the weather is totally great for light walking, for distance observing of the mighty Himalayas, and for tasting various sorts of local and imported tea in Bhutan.
December is a quite warm month in the lowland country, but in January and February daily temperature may fall slightly below zero and occasional snowfall covers houses and roofs with a thin layer of snow.
It is not recommended to go climbing in the Himalayas at this period, but visiting some valleys across the Bhutan is a great experience in Winter, especially if you choose the right timing. For example, Phobjikha Valley welcomes rare Black-Necked Cranes in December and January. Also, newborn takins come to this world in February, so you may enjoy this natural miracle in Motithang Takin Preserve in the capital of Thimpu.
Winter is probably the least busy season for tourists and you may be able to get some great discounts accordingly.