Is getting dry during sex with my husband a sign of perimenopause?

Could be? There are reasons for vaginal dryness. Adequate foreplay and arousal is important, however, hormonal stimulation is needed too. If concerned, your pcp, gynecologist or other provider can check hormone levels. What is your general health and what medicatons are you on. There are many preparations available for vaginal dryness to help aid you in pleasurable intercourse.
Possible, unlikely. Vaginal dryness is a common complaint of women during menopause and it may even begin during the peri-menopause. However, it is unlikely that a 33 year old woman would experience either. You may find it helpful to use one of the many female vaginal lubricants that are available over the counter.