Roaming will be banned in 2017, and from April 30, 2016, surcharges for
roaming will be capped at a maximum of €0.05 per minute for calls, €0.02 for
SMSs and €0.05 per megabyte for data.
So in fact €1 = 20MB, or assuming a typical instagram image is 250KB, 80 instagram images. That's still pricey in my book. Background app updates... 200MB please, that's going to be €10.
The point is that international roaming is generally expensive right now, the EU is now mandating a transitioning plan to free roaming with an intermediate rate cap which is most likely an improvement over existing EEA rates (my ISP's lowest EEA rate at the moment is 0.06€/MB)
Alas, you can't get a subscription as a foreigner (or at least, not easily). But you can get a relatively cheap, pre-paid SIM, which works just fine.
A lot of vendors at BKK (or any other airport) will be more than happy to sell them and configure your phone in the process.
They're also quite useful for reasonably priced phone calls home if you don't want to dicker with Skype and they can be topped up at just about every grocery store.
Anyway: Thank you for the tip. May it be useful to other travellers.
In the past it was not uncommon to get a €100 bill if you used your phone on vacation like you do at home. But it has become cheap enough that you do not really have to worry about it when you are on holiday for a week or two.
It doesn't make clear though if you will be able to use your program with roaming from April 2016 —they say explicitly you will be able from 2017.
Data charges without a data-plan are very expensive. Also it isn't still clear what will happen on prepaid card numbers, which many people choose as the only way to have a pay as you go service with reasonable charges.