'Though I was lying in bed, I could feel the strong wind blowing on my body' is better. Switching tense there doesn't really work, and you need the 'on' as well.

Typically, one doesn't feel "wind" in bed. Indoors, "wind" is called "a draft" or perhaps a "breeze". So then it would be "While I was lying in bed, I could feel a strong draft"... unless, again, you're trying to speak in flowery language for artistic purposes (and if you are, then you can go into more detail with "blowing against my body" or "running across my legs" or whatever you want). But if you're just trying to communicate what happened, you would just say "I could feel a draft" or "I felt a draft".