White is great for overwintering use.
White lowers transmission of light
and thus heat buildup during those warm and bright winter days,
helps prevent the trees from budding out too soon.

White generally has a transmission value of 50% or less,
clear green house films are in the 85%+ range.

Rule of thumb,
reduce light transmission by 1%
it reduces plant growth by 1%

So you can reduce heat by limiting the light and plant growth with white plastic,
or  use clear plastic and ventilation to deal with the heat.

Whatever material you choose for the roof,
remember the snow load, make sure the material can handle it.

The roof of our sun room is twin wall polycarbonate, same as Tom used and Chivas mentioned. I don't know when it was installed, I have to guestimate maybe 15 years ago. It has handled huge snow load with no problems whatsoever.  In the last two years it has started to degrade and is starting to take damage from moderate sized hail. Panel replacement is on the to-do list for next spring.
In the future, if I were to build a sun room on a new house, I would use the same plan and materials. And as Chivas said, it really does well keeping the heat in.