Despite the dreary weather, Suri didn't let a little rain wash out her big day ... she happily chatted away with her pal while under the shelter of her pink umbrella.

Suri had a gift bag in hand during her walk around town, suggesting the celebrations were already underway. It remains to be seen if there will be any larger festivities later -- she leads a pretty low-key lifestyle -- but ya gotta figure her mom Katie Holmes has something planned for such a big birthday.

As for Suri's dad, Tom Cruise, he most certainly won't be joining in on the birthday fun for a couple reasons.

First of all, Tom's across the pond from Suri right now -- he's busy filming a new project in London.

But, more importantly, the father and daughter reportedly haven't had a close relationship since 2012.

In fact, the last time they were publicly seen together was at Disney World that summer. That's also the same year Katie filed for divorce from Tom, when Suri was just 6-years-old.

At this point, they've been estranged twice as long as they were together -- so, the Tom factor's probably NBD for her.