You might want to rethink your plans. On Mar 2 of any year, you would not be able to drive from Flagstaff to the Grand Canyon Lodge, which is on the north rim, which is closed mid-Oct through mid-May each year.

You indicate you are going to be hiking down the south kaibab trail. This is on the south rim side of GCNP, not the north rim where you wanted to stay.

Your hike doesn't make sense even for starting from the south rim. Are you taking the South Kaibab trail to Bright Angel Trail? Or BA Campground (at the bottom of the canyon on the north side of the colorado river)? If the campground, you will already have crossed the colorado. Next you indicate taking the bright angel trail to the north rim. The bright angel trail is on the south side of the river and runs from the river to the south rim. If you mean the old bright angel trail, you would need to be a backcountry expert. But again, you wouldn't want to take it in the winter since the north rim would be heavily snowed in. And the road out is closed, so even if you hiked to the north rim and camped (carrying all of that winter gear), you would have to hike back down to the river and back up to the south rim to get out, unless someone was meeting you at the north rim with a snowcat, or you were carrying your cross country ski's up to the rim and were going to ski the 45 miles to Jacob Lake, and have someone meet you there to drive you to Page.

Check out the park service website at www.nps.gov/grca and for hiking info, www.hitthetrail.com

Good luck!

Thanks for the detailed comment - much appreciated.  I've updated my plans as appropriate.

I always intended to do everything from the Sth Rim - I think my plans make sense now.

Checking out www.hitthetrail.com now - many thanks for the link!

Glad I could help.

For in-park south rim lodging, the authorized concessioner to the park service does have online booking (no added booking fees, and a liberal cancellation policy of full refund if cancelled at least 48 hours prior to arrival). The website is www.grandcanyonlodges.com

It also has information about staying at Phantom Ranch, at the bottom of the canyon - but you'd have to book that either by phone, or by submitting a request form that's on that website.