In reply to Jimbo W:
We had our firstborn out on the hills a lot, including the Paps of Jura when she was 3½ months. That was a freakishly warm, not too windy period in February; we didn't take her out much in winter.
At that age, we found a fabric sling to be best, as it keeps them warm and allows a few different positions. Here it is, when she was 5 months old:
http://www.dreamsofmountains.co.uk/freyaca/20080427Jen_Freya_Stob_Breac.jpg
In a sling, you can easily hide them from the sun (face inwards), and the cold - providing it isn't too windy.
We were out in showery weather a fair bit, but not in pouring rain. If they have an all-in-one rainsuit, the wet isn't really a problem.
I wouldn't take a young baby out when it's very windy, as there isn't as much you can do to protect them from that.
Remember you'll have to take them out of the sling/carrier to feed them and to change them, so keep that in mind when considering the temperature and windiness. Also remember that they may not be as warm as you, as they aren't exercising.
We took our secondborn (approaching 3 months old) up Creag Bhalg by the Linn of Quoich yesterday, along with our firstborn, who at 2¾ years can now walk a fair bit of it and goes in a Deuter Kid Comfort II or on my shoulders for the rest. It's slow going with two, but at least there was no need to worry about the cold yesterday!