Wow, thanks for all this help! Very cool...
Yes the second tree had some small white/off white flowers in Spring- they didn't last long however.
The first tree (bald cypress?) was indeed bald when we were first looking at the house during end of last Winter... I will watch it this time and see how soon it starts happening. Here's a few closeups of the first one's smaller end branches, although it seems we have an ID... Next are a few closeups of the second tree. Note that the second tree's leaves can get as large as the ones showing against the trusty old ruler. Thanks!