He did put in a provision to prohibit federal agencies from hiring contractors. From the order: "Contracting outside the Government to circumvent the intent of this memorandum shall not be permitted."
I haven't seen a single fake news site report that though, they are all pushing the alternative fact that contractors will be hired en mass.
Stuff still needs to get done, so a hiring freeze means needing a workaround, they will find money for contractors because it is seen as a limited time expense, even though it is probably 3x or 4x more expensive over the long term. When they tell you they cut the size of government they won't tell you that government costs went up, or they will tell you government payroll is down and contractors get costed as something other than payroll.
In software it never works like that. Costs more to build it with contractors and then because you get rid of the contractors support is done by people unfamiliar with the code so support costs more, upgrades cost more because new contractors need time to learn the codebase or the old contractors charge more because they know the codebase.
Bonus: when Trump "freezes the size of Federal employment" do you think that will be match by a freeze in contracting, or a boost in crony contracts?