Would it be possible to ride the solar wind into space?

Solar wind particles are absorbed by the atmosphere.  There are none from the solar wind down here on Earth.  So you cannot ride the solar wind into space.

Now if you mean can you use the solar wind to travel through space to some destination like a distant planet or another solar system--maybe.  That is called solar sailing.  Stretch out thin, thin sheets from a small spacecraft, and let sunlight and the solar wind particles push it so gently along and away.

Even can help that probe along with laser beams for faster travel.  There is already a test probe doing the solar wind propulsion idea.  But for a large spacecraft that could carry humans any distance--the sail surface would have to be many miles across.  We don't yet know how to build that.

You cannot ride the solar wind "into" space (from the Earth) 

but you can ride it after you are "in" space, and outside of 

Earth's atmosphere.

You need a special space suite to ride with the solar wind that would bring you out of the solar system.

You get into space, then deploy a large enough solar sail for acceptable propultion, yes, it would be possible.

Problems like here on earth with a magnetosphere would mean alternate propulsion.

Asking if this is practical, I ask why our deep space probes are not set up with solar sail.

From Earth's surface, no..Once you get into orbit and deploy a solar sail, yes, very possible

According to scientists the solar wind can form parallel dimensions

Yeah if you want to die