Hardly. Twitter and Facebook aren't private in the least bit. They are both PUBLICLY-TRADED companies on the stock exchange.
ALSO, BOTH of these companies have CLEARLY risen to the level of being PUBLIC UTILITIES used for mass communication and in many cases the SOLE media by which certain information is broadcast and shared (Fire/Police Depts, etc)..
AT&T, Sprint, & Verizon, are not permitted to censor your phone discussions and neither should Twitter and Facebook!
Trump's exec order can only involve the exec branch or declare a national day of prayer - that sort of thing. I think it will be more along the lines of ordering the DOJ to investigate whether they are too big and should be split up, such as IBM and Ma Bell was sued by the government on the last day of LBJ's term and the suit was active into the 80s - or investigate the possibility they are public utilities subject to regulation (despite the law suit - things change) - or perhaps order the FEC to investigate election tampering...or all of them. I think that is where it is headed.
Trump just can't order them not to censor - it doesn't work that way. He is not a dictator and the law certainly doesn't support him in that effort.