Yes, occasional naked walks in the eastern part. People often say it's busy in the Forest but most of my walks (clothed or not) I never meet anyone apart from deer. Most people stick to well worn tracks and don't venture too far from the car parks. I'm happy to wander anywhere and get lost as I know my area well and have a good sense of direction.
Weekdays, particularly evenings can be very quiet and the last hour of daylight can be quite special on a warm evening.
Sundays you get joggers, even at 7am, but they'll stick to paths and tracks.
Things to watch out for include ; insects, parties of bird watchers, horses, cyclists. Ticks (allegedly) but never had one.

I found a place that seems quiet enough and wrote about it here. Not that familiar with the detail but I think north of the A31 is more promising? Went for a walk south east of Burley during the summer and it was heaving but things should be quieting down.

The SOC did a twelve mile walk in the New Forest last Thursday! Exhilarating - and very few people encountered!