I took the bus from Madrid to Segovia (and back) on 10/22 and it was tremendously easy. From everything I've read, it's best to forget about the train and hop on the bus. If I remember correctly, the bus is cheaper, faster and drops you off a lot closer to town. I think the buses leave every half-hour (in both directions).

Enjoy Segovia...

If you're taking public transport, the bus is a better option. The train station is not centrally located, you will be taking Cercanías, which are also known as "pueblo-hoppers" as they stop EVERYWHERE unless you get on certain ones, and the bus station is at the end of the main (now pedestrian) street in Segovia on Paseo Ezequiel González...very close to everything.

Although I prefer train travel to bus travel, in this instance, and in the trip between San Sebastián and Pamplona [totally unrelated], I recommend the bus.

Two years ago I made this trip by train. We passed through an area with early snow in November. It was beautiful. I hope you have the same experience.