How frequent are touch-and-gos?
In larger aircraft you may not be able to execute a go around once you have touched down but its not always because of weather. This mainly has to do with the fact that once a plane touches down (situation depending) it may have already committed to the landing and will no longer be able to get airborne with the remaining runway. There is a discussion here on the topic and an article here that covers it as well. 

It generally takes more distance to take off than land and a considerable amount of speed is bleed off during the flair and subsequent touch down. If a plane touches down at the proper touch down point on a runway it may not have enough distance to accelerate and become airborne again by the other end of the runway. Further more you can complicate the situation with things like thrust reversers which, once deployed force you to commit to the landing. 

The airport in question has a 5578 x 98 feet runway which is a solid size but chances are you were flying a plane on the smaller side. Generally the smaller the plane the less runway you need to land and take off so go arounds after touchdown are possible. 

To directly answer your question, in some instances they do happen but they will be recorded as an aborted landing. In other cases (heavy crosswinds) you may have only one side of the mains touch (does that count as a touch down?). The runway length and aircraft size/performance are the main factors and there are so many combinations of that.      

--Edit-- 

Since you have provided the make and model of the plane we can extrapolate a bit more. You can find the full specs here but lets take the the At TOW for 300 Nm - Max pax - 3,000 ft - ISA +10 - situation which is quoted at 4,626 ft. Take off speed at max load is 116 Kts (and you were landing so you were on the lower end of the fuel which means you were below max load even with full passengers). Likewise approach speed is 113 Kts. Some of this depends on the pilots precision but It should be (and obviously was) possible to touch down, full power, and get airborne again in enough distance on the strip. Sine you would only need to make up 3 Kts assuming he came in on the mark at 113. They would lose speed in the touch down but if they were on the throttles fast enough it would work.