I never used Terebene until Jan 2010. That was when the EU reduced the levels of VOCs in paints. I was painting cabinets in a regular customer's home. The next day the oil based eggshell paint was still tacky.
I have seen people state that driers make the paint more brittle. After 15 years of using terebene both indoors and outdoors, I have not seen any evidence of paint failing prematurely or not. That said, oil based paints in the immediate aftermath of the 2010 VOC compliance were awful to work with. It took 2 or 3 years for the likes of Dulux to improve the formulation.
Apropos grey waterbased undercoat, I have only ever used the waterbased versions when priming MDF prior to applying dark green colours (eg mid Brunswick green). To be honest, I found the regular Dulux Trade grey undercoat/primer to be easier to sand back than their white version, it did clog the abrasives, but less so.
Personally, based on person experience, at cold, rainy times of the year, I would rather apply oil based paints. A couple of years ago I applied DT Weathershield masonry paint on a cold day. It wasn't forecast to rain for 5 hours. The rain washed away some of the masonry paint (onto the paving...).
On reflection I should have applied oil based masonry paint.
In short, rain will wash away wet waterbased paint. Oil based paints, heavy rain might leave slight dimples in the finish (which can be lightly sanded back when the paint is dry).
In my experience, light rain makes less difference to oil based undercoat than waterbased undercoat. Oil based undercoat is a different proposition to oil based gloss. On horizontal surfaces, heavy rain creates craters in soft (read: wet) gloss paint, the edges of those craters become dirty really quickly. I have never quite understood why. Annoyingly, one has to wait 3 or 4 days to sand them (the edges of the craters) back with 180-240 grit silicone carbide paper flat