Outside Madrid: Walks in the Mountains?

With all this great weather we are having, I would kinda like to get out of Madrid once in a while and go walking in the surrounding countryside. Does anyone have any suggestions?

Also, is there anybody else who would be interested in the occasional weekend jaunt out of town, stopping for lunch somewhere enjoying the traffic free Spanish countryside?

My main concern is safety (it is still winter and there is snow on the ground in places), there are pleanty of horror stories in the UK of townies wondering off thinking everything was hunky dory just because the sun was shining, and end up getting lost with or without broken limbs.

It's difficult to get lost in Madrid mountains. There are many tracks painted with sings you just have to follow them. Most of the accidents come because of the ice or because people goes out with bad weather. With days like this you won't have any problem.
Some places you can go by train to beguin walking are
Cercedilla (you have to walk 20' by the road until you get to the tracks, you have 3 different tracks to go up, and there is a forest center where they give you information.
Navacerrada and Cotos, you have also several tracks, going up to Peñalara, or going down from Navacerrada to Cercedilla.
By bus you can go to Rascafría, very beautiful too, and there's another forest center where they explain you the different tracks.
I think it won't be possible for me to join you by now, but if you want more information ask it.