SAC is a Type 3, prune back hard each year, so I would cut it back. The vines can be left each year until close to spring and the birds can still use it for winter cover.

This clematis is considered invasive in many parts of the US. Some people cut the vine back right after flowering to prevent seeds dispersing via wind and birds.

I agree w/ mnwsgal ~ At the advice of a SAC owner from WI ~ the beautiful mass of hair catches strong winds! Almost prophetic ... just before I could cut back mine that very year, a late Fall tornado took my SAC down arbor & all ~ sigh!!! Like you, I wanted to leave it ti' early Spring, for winged friends' refuge but left it just the year before the tornado took her down.

About the seeds sprouting ~ not too bad here, but I have found a few seedlings around. A nice haircut after the blooms are done would be what I'd do!!!

SAC is not easy to kill ~ I've since move mine fom pot to ground & pot to ground again in different sites ... stll going strong altho not as huge as before she was taken down by tornado ~ she will soon again if I leave her where she's now!!!

FWIW