Per Yoreh Deah 241:3 one should not take out a thorn embedded in his father as it may cause a wound. One should also not do a phlebotomy on his father. I have heard people saying that this would extend to haircuts also as at times it may lead to slight bleeding. Is there a source for this one way or the other?
Leket Hayosher Yoreh Deah page 37 says that it is prohibited since it may cause bleeding.
However in the Sefer Moreh Horim U'Kevodom 10:12 it brings down in the name of Rabbi Ben Zion Abba Shaul Zatzal that a son may trim his father's nails and cut his hair.
Also the Debreziner in Shaalos U'Teshuvos Beer Moshe 4:84 permits a child to cut his fathers hair.