Matt Lauer All Smiles with Estranged Wife for Their Daughter's Sake

Matt Lauer looks like he's getting along great with his estranged wife -- smiling and having a grand ol' time, bonding over their love of horses ... that are ridden by their daughter.

Matt and Annette Roque were grinning Wednesday morning as they cheered on 15-year-old Romy ... who's competing in The Hampton Classic Horse Show.

By all appearances, Matt and Annette are comfortable in each other's company, despite their divorce, which is nearing completion. It's the first time we've seen the former couple this chummy together in public since the split.

Mom and Dad getting along is good news for the kids ... even though their son, Thijs, doesn't exactly look thrilled. We'll chalk that up to healthy sibling rivalry ... or maybe the giant purple ribbon. Or, the scent of horse crap.

As we've reported ... Matt and Annette split up back in 2017, after Matt was axed from 'Today' over multiple sexual harassment allegations at NBC.

Matt's not getting back on the horse, professionally, yet -- but the fam's looking good.