“Kid: You look like Max Headroom!
“Carter: No, He looks like me.”
— Max Headroom (TV show)

No.

The only particle that could be said to “have” a Higgs field is the Higgs particle. Technically, though, it’s the other way around: the field has the particle.

Other particles do not have the Higgs field… elementary particles interact with it. So the Higgs field affects speed of elementary particles, by providing the mass of elementary particles. It is not the only thing that affects the speed.