First question. When you say "windows" (plural), are you referring to windows in the side wall? Or the slatted window in the front wall, under the stone guard?
If you are referring to a side window, the following troubleshooting questions may help.
Is the sliding pane closing completely? Or not quite? The little plastic latch piece should snap closed over the mating piece. This is sort of common. However, an incompletely closed pane would probably leak along one of the vertical edges, not over the bottom edge.
Onward. When you say the wind is coming in "around the bottom of the windows", do you mean around the edge of the glass within the frame? If so, is the wind coming in around a sliding pane or a fixed pane? The seal around the fixed panes is easily viewed - just check it out. The sliding glass panes ride within a track (slot) which is lined on all sides with a fuzzy cloth-like material - black, as I recall. Can you see this lining in the sides and top of the track? If so, is it missing or compacted in the bottom of the slot?
Or is the wind coming in around the frame where it contacts the wall?
If the wind is coming in around the frame, then either the outside caulking is damaged or missing, or the frame-to-wall seal, either inside or outside, is damaged or missing. The first is easy to visualize, and not hard to fix. Just renew or replace the caulk. It is harder to imagine how the second would occur. But if it has, you will likely need to remove the entire window from the wall (not terribly difficult) and clean off the existing seal and replace it.
If you are referring to the front window, that is a different question. Let us know, and we can continue.
Bill