Blue Jays are throughout north Texas, and as Texans know, Blue Jays are particularly fond of acorns (we live in a "post oak savanna). This fondness is mostly responsible for the rapid spread of oak trees after the last ice age. They are able to hold several acorns at once, while flying.
Do north Texas woodpeckers migrate? Some do -- some don't. Muddy answer I know (but true). Of the 22 woodpecker species north of Mexico, only 15 migrate long distances.The others don't migrate at all, or are "partial migrators" - just moving into a nearby valley, or something like that. Non-migrators include the Downy and Hairy Woodpeckers, and the Red-bellied Woodpecker. On the other hand, our local species of Yellow-bellied Sapsucker (a member of the woodpecker family) spends summers and breeds up north and migrates here for the winters.