Clearly not everyone here is aware that even small rifle primers come in magnum versions. A small rifle primer has plenty of brisance to ignite a .308 Win load (43-45 gr) in Palma brass unless the temps are below 20-25 degrees or so. There are so many other factors that go into ignition...it's not just small versus large rifle primers. Small rifle primers come in magnum versions as mentioned, and there can be a very wide range of brisance between different makes. Some are simply hotter than others. In addition, Lapua .308 Win Palma brass has a 1.5 mm flash hole versus a 2.0 mm flash hole on their standard .308 Win brass, which certainly has an added effect above and beyond the differences between small and large rifle primers themselves. Some brass manufacturers, such as Alpha Munitions, use a 2.0 mm flash hole in their .308 Palma brass. The bottom line is that you need to know exactly what you're working with. That includes the brisance of the primer you're using, the flash hole diameter of the case, the type of powder (i.e. ball versus extruded), etc.
Someone wishing to use .308 Win Palma brass in temps where ignition may be an issue should consider using a magnum primer such as a CCI 450, or some other type of primer such as a Rem 7 1/2, which is known to be a relatively hot primer. Using a brand of brass such as Alpha, which has the larger flash hole might be beneficial. Avoiding the use of ball powders, which have a reputation of being more difficult to ignite would also be recommended. Finally, if the intention is to use such a load in cold temps where ignition might be problematic, it would be very wise to do some testing at the practice range under similar temperature conditions to be sure the chosen combination was actually capable of reliable ignition.