Three main seasons in Thailand, but as everywhere the mountain areas will have more extremes of weather. I give you my experience, rather than text book stuff, and the start and finish of these seasons does seem to move about a couple of weeks or so each year. Below applies to North and North Eastern parts. The South is different again.
Now - rainy season, from sometime in late July or August through Sept, finishing late September or early October.. Rain can come at any time of day, and can be very heavy with Thunderstorms, but also spells where no rain for several days. Often have dry days with cloud building up and rain early evening or nighttime. Daytime temps can be quite hot, 30C to 35C and does not cool too much at night, so sticky nights.
Riding in this season means avoiding the rain, but has the benefit of clear air, beautiful green scenery, and often dramatic skyscapes. Can be safety issues, with lightening, floods and sometimes mudslides in the mountains.
Next comes the winter season, starts sometime in October, or even early November, the rain gradually drops in frequency and intensity, the nighttime temperatures start to drop, although days do not seem much cooler. December and January are generally dry and can be quite cool at night and early morning, especially in the mountain areas. Definately some warmer clothing needed for riding then. Frost has been seen on the mountains, and becomes a must see thing for the Thais, ice never becomes a problem on the roads.
By February the green appearance has become dusty colour and the waterfalls are not too spectacular. During February things start to warm up a bit, maybe an odd shower, and this process continues through March, by late March and April it is getting really hot and the summer has started, the showers increase, but are usually a welcome relief. The summer is probably April till July and back to the rainy season again. The North does see problems in March and April with the burning of hillsides and consequent smoke and air pollution, this destroys the views and can even be a health hazard in Chiang Mai and district at times.
So for a once off motorcycle tour of the North, November, December and January are probably favourite months for avoiding the rain, having cooler nights and normally reasonable riding conditions on the road.
Also the time many tourists come, but this may make the cities busy, but not usally a problem on the roads out of the cities.
I ride all the year round, even the rainy season, because the scenery is so vivid and dramatic, this time of year, but would not plan a long tour until a little cooler and less rain.