Yes, it would be possible. Almost anything is possible if you throw enough resources at it.
The question you probably intended to ask was: Would it make sense to (...)
And no, it wouldn't. The added weight for an actuator, hinge with aerodynamic fairing, structure etc would cost you more than the arguable and very marginal benefits. Besides, winglet design is an art. It is very hard to create a winglet which will actually give you an advantage for the type of flying done with a given aircraft. In fact you can easily damage performance with a poorly designed winglet. If you tried to add the option of folding it down to act as a raked wingtip, you'd inevitably end up with a whole lot of design compromies, making a really poor winglet which would fold down to make a really poor raked wingtip.
I thought I was doing good trying to avoid those airport hotels... and look at me now.