What does your HR strategic planning process look like? Onsite? Offsite? Homework then share? Group collaboration? I'm curious what other organizations do.

Collaboration over the strategy is crucial in my opinion. It aids buy in and also ensures that all bases, barriers to success and enablers are considered. 

When I revised the L&D strategy I had an outline of my view point and then engage the team face to face in how they saw our success factors, priorities and what this looks like as objectives to succeed. 

Offsite; often some pre-work - some questions to ask of local leadership teams to try to get to the root of business priorities as they relate to people; mix of bottom up (previous point) and top down (macro and global business strategy) thinking; develop with HR group, then test with leaders to iterate; refresh every year.  Hope that helps :D