As it happens, I was looking at what to buy next for the Saxon army. I've already got the three Chevauxleger regiments and the Leib-Carabiniers who avoided the surrender at Pirna and who then fought with the Austrian army.
I'm just getting started in this period, but got interested after visiting the Sächsische Schweiz, where the fortress Königstein is. But I've a lot of research to do, my area (profesionally and gaming) is the Migration Period, so I'm not as familiar with this, but since the Saxon army was relatively small and I'm in the area so it strikes my interest, I thought it would be a great starter project in this era.
Sorry mate, I started typing as the taxi arrived and the wife started shouting at me...

Yes, as mentioned above, the three Chevauxleger regiments and the Leib-Carabinier Regiment that fought with the Austrians are an excellent investment, as they performed sterling service and fought in two of the most famous battles of the era - Kolin and Leuthen. They're also very pretty!

There were also two excellent regiments of Uhlans, but they didn't fight in the major battles, being mainly concerned with reconnaissance and the 'petit-guerre' of raiding and skirmishing.
After the mass-surrender at Pirna, Frederick outraged Europe by forcibly conscripting the captured Saxon Army into the Prussian Army. Most of the Prussian regiments conscripted in this manner suffered terrible problems with discipline and associated desertion, with some units deserting en masse. In the main they were used as garrison troops, though one or two proved more reliable (e.g. Prussian Infantry Regiment 55 'Hauss' and the two formerly Saxon squadrons added to the Prussian Gardes du Corps) and served as part of the field army.
As the trickle of Saxon deserters became a flood, the Saxon Army began to reform in exile, re-adopting its old uniforms (minus the mitre caps) and serving as an auxiliary corps under French command. However, the reformed Saxon Army was mainly infantry; hardly any cavalry or artillery units were re-formed (the Chevauxlegers, Leib-Carabiniers and Uhlans continued to serve under Austrian command).