There are summer thunderstorms, mainly in the north and north-east between February and April. They tend to be isolated at first, then become more widespread, especially after Songkran. The occasional thunderstorm may hit central Thailand including Bangkok too, but in my experience, they tend to be more widespread and stronger up north and north-east vs Bangkok during that time of year.
Then, around mid-May you start to experience almost daily thunderstorms, which last into early June. That's followed by light or moderate rain, generally without thunderstorms, until early July when there's a mini dry season lasting 1-2 weeks (speaking of Bangkok and anywhere east of the Dawna range). West of the Dawna range, along the border with Myanmar, it's far wetter and June, July tend to be VERY wet.
Mid July until late September tends to be rather wet in Bangkok and much of upper Thailand.
2021 was VERY, VERY wet in Bangkok at least, beginning in mid July and lasting until mid September or so, but the wettest period was during the Tokyo Olympics until roughly, mid to late August.
Depending on the year, the rain reduces significantly starting in the 2nd to 3rd week of October. This year, at first it seemed like the rainy season was over around September 27 or 28, but a few days later, the rains returned. While it's been mostly sunny most days since the second week of October, there has also been a bit of rain here and there and it continues to be humid, so feels like the season change isn't going to be upon us until maybe mid November this year.
Unusually, February 2022 was very wet, with 10 consecutive days where there was some rain, at least in central Thailand. All the smaller canals filled back up and the humidity was as high as in September, so it can definitely rain at anytime of year in this part of the world, even during the so called "dry season".
As for cold exposure - this is only an issue at higher elevations or sometimes, in the north or north-east among poor, elderly villagers who can't afford blankets or warm clothes and live in houses, which get cold during the night in those areas during December or January cold snaps because they aren't insulated.
The south has a different climate, with a second, wet monsoon season beginning in December, particularly on the east coast.