No - Boston ivy's deciduous. It's also quite hard to kill
The first clematis is possibly a montana, which looks dead at this time of year until you get the little shoots appearing at the leaf joints. A well established one will be absolutely fine, so don't worry too much. You should see some growth soon.
Check the other one by scratching a little of the 'dead' looking woody part. As has been said, if there's a bit of green there, it'll be fine. Water is essential for good clematis growth, so if you're in a dryish area, or the clematis is in a dry part of the garden, just make sure it's watered in long dry spells, and add a mulch afterwards to keep it happy.
In any case, if you don't know what varieties they are, wait till they flower and post some pix, and you'll get a bit of help with the ID. That will help with the pruning regime and any maintenance in future.
I'm wondering why the Boston Ivy has a trellis - it's self clinging, so no need for any.