I don't know about 2000MR, but I've had pretty noticeably awful results with .308 Palma/SRP brass and Varget in cooler temps (<40F) at distance (300-1000yds) in F-TR competition.
Bear in mind, I'm not talking about hopping out of the truck and doing load development, etc. - my fingers are the limiting factor in the cold long before the ammo is, in that situation. In fact, I do my early season load dev in pretty much exactly those conditions every year in order to get ready for the SWN, with no complaints.
Specifically the times I've noted severe accuracy issues were where the gun and ammo were left overnight in the truck in cooler temps (Raton, NM in September) or where the ammo was left unprotected in the box on the line all day long in crappy weather.
Once the problem was identified, I started leaving the ammo on the dashboard with the heater going for a while, and keeping the next 22 rounds in my pants pockets next to the 'boys' (BRRRR!!!!) while I was down in the pits pulling targets, or up scoring / waiting to shoot. Other times I've put the whole ammo block in a small insulated lunch box with some hand warmers. Either way worked.
For .223, I'd expect the problem to be less of an issue, both because of the relative size of the powder column, and because of the large flash hole.