My partner and I walked the meseta from Burgos to Leon in February a couple of years ago and it was marvellous. Although the meseta is uniformly elevated, it doesn’t have very high peaks as say, on Day 1 out of St Jean, or later at O Cebreiro, etc, and so is less likely to have snow, which is always a possibility at that time of the year.
In fact, the weather was ideal for walking, clear and around 15 degrees. There were very few peregrinos, and some small villages were entirely zipped up, nothing open, not a soul to be seen. But there were enough places open for a halfway coffee each day, and the small hotels/pensiones we stayed in each night were wonderful: warm, welcoming, dinner available, and friendly locals to chat with.
We'd flown in to Madrid, taken the excellent Alsa bus direct to Burgos, same for the return from Leon.
Buen camino.