Those altitudes are FAR above terrain, but you can still get some "interesting" winds.
I've no experience in a Saratoga, but other Pipers really don't seem to like altitudes over 10,000, even light. If I were you, I'd take it over some place closer to home like Banning Pass up to 12,500 and see how it does (and how you do -- oxygen may be an issue even if it is not required by reg -- take a pulse ox). If it takes 30 or 40 minutes to climb up there from sea level, do a canyon crossing on a severe-calm morning, only.
7000 feet is nothing compared to 12,500 in a naturally aspirated small aircraft. Big Bear can get hairy in the wind, but it's really easy in calm winds. I took a Warrior there once, with the DA sign at the run-up area reading 8500.
Know your V-speeds at altitude. As you get close to your service limit, you'll need to fly closer to Vy to maintain altitude. And Vy will be lower at those high altitudes. It often appears in the POH at 10,000. You may have to extrapolate to the actual DA.