I've noticed that winglets are very rare on small aircraft. I wonder why this is the case. Wouldn't they have the same advantages, especially because they travel at low speed? Or is it just a wrong impression I got and they aren't that rare?
I've talked to a couple of aerodynamicists, and for small aircraft when you run the numbers the improvement offered by winglets is often less than the drag penalty caused by their weight (which also reduces allowable payload). For larger aircraft that fly long distances, the proportion of the aircraft's weight that is due to the winglets is much smaller than it is for small aircraft, so they don't have this problem and that makes winglets a viable strategy.
As others have pointed out winglets don't make much aerodynamic sense for small aircraft.
The point of a winglet is basically to deflect the wingtip vortex away from the lift-producing part of the wing, granting an increase in effective wing span without the added form drag of actually making the wing longer.
The winglet itself creates some form drag though, and it adds weight. On most small aircraft the potential improvement in wing efficiency doesn't exceed the weight and form drag that result from adding the winglet.
What you will find on many small aircraft are Hoerner-style wingtips (either installed at the factory or added later through an STC modification). At lower speeds these have aerodynamic benefits similar to winglets, but without the additional form drag, and usually little or no added weight.
First, winglets look fancy but will not help that much in drag reduction. They were pushed less by engineers than by marketing, Boeing's in particular. They help a litte in ideal conditions, but in sideslip or at high speed they can quickly increase drag.
Then, most small aircraft are designs from a pre-winglet era. Adding them means to invalidate the type certificate, unless someone takes the initiative to re-certify the aircraft with winglets. I guess nobody has seen this as a profitable endeavor so far.
Gliders benefit from winglets because in competitions they are grouped in classes. Membership of some classes is defined by wingspan. Gliders get better with increasing wingspan, so if regulations limit the lateral extension, the way out is to extend the wings upwards. If there is no such artificial limit, it will in most cases be better to expand the wing in spanwise direction.
Many small aircraft designs are rather old and winglets were not common on airliners either when they were certified. For airliners that fly 8 or more hours a day saving a few percent on fuel quickly pays off the additional development and certification, so winglets were adopted quickly there. But typical general aviation aircraft does not fly anywhere close to that and the few that fly more and would be worth upgrading (and their owners have money for upgrade) are not enough to make the design and manufacture profitable.
Note, that winglets did find their way to gliders, especially competition ones, as the little benefit is more noticeable there. They also do appear on some newer designs, most notably the Diamond ones (DA20, DA40, DA42).
The situation is very similar to why we don't see more aircraft diesel engines. They are more efficient, use cheaper fuel and are somewhat cheaper to maintain, but the certification is so complicated that there are only few modifications available.
Also most GA aircraft are not really very efficient to begin with. The DA20-A1 claims glide ratio 14:1 and that is way better than most competitors. Compare with airliners where 18:1 is nothing special (was claimed by A320 some 30 years ago). So winglets are not going to help as much.
One possible explanation is that large amounts of sweep and higher indicated airspeed are less common in "smaller" GA aircraft. Larger and faster aircraft with large amounts of sweep literally plow the air aside, resulting in a significant spanwise airflow at the wingtips.
Winglets are touted for reducing the strength of wing tip vortices, and are said to generate some forward force from the wingtip vortex, but they also may improve efficiency simply by bouncing the span wise flow aft, which would generate a small amount of thrust.
The winglet "fence" may also allow a slightly lower AOA for the same amount of lift by helping maintain pressure differential all the way to the wingtip. Lower AOA means less drag.
An earlier form of winglets, wing tip fuel tanks, also served as a wing tip fence in addition to acting as a wingtip weight roll damper and spanwise weight distributor.
Many smaller, slower planes do not benefit enough from winglets to justify the additional cost and weight. However, they may be seen on STOL aircraft to help trap a bit more air under the wings for high AOA slow flight, along with slats and flaps; and more competitive gliders, where a slight advantage is meaningful.
My general understanding is that winglets are most beneficial for aircraft that spend a lot of time in a rather narrow window of possible angles-of-attack-- e.g. an airliner in long-range cruising flight. Small aircraft tend not to fit this profile, unless they are flown by really boring pilots.