Hi Emily!  My husband and I just moved to Dallas too.  We've been taking Winston to the Wagging Tails dog park on Keller Springs road.  We lucked out living down the street from it.  Its really nice, they have a small dog area and a big dog area and lots of room for the dogs to run around.  We've only gotten to take Winston once but can't wait for it to get a little bit warmer so we can go way more often.

theres a great new dog park in lewisville at railroad park, also denton has a big dog park called wiggly field

We frequent the park at at the Lewisville RailRoad Park.  It is fairly new but it does have both small and larger dog areas.  The trees are still new so not much shade,  There is a covered area in both parks.  We had gone to a the park in the Plano area that was really nice.  We are going to go to the park off of Keller Springs so looking forward to it!