1. If I take off this current insulation is the basement going to be a lot colder? Blockquote

Probably. It's difficult to estimate without knowing the indoor/outdoor temperatures of your home, construction of your home, R-value of insulation, etc.

Is it a bad idea to get rid of it even if it hideous? If so is there a cheap idea for insulating without framing? Blockquote

I wouldn't remove it because it's serving a purpose. If it's an unfinished basement, what does it matter if it's ugly? I haven't seen a great looking insulation. If it were me, I wouldn't worry about it, or finish your basement.

If I take off this current insulation is the basement going to be a lot colder?

Probably. It's difficult to estimate without knowing the indoor/outdoor temperatures of your home, construction of your home, R-value of insulation, etc.

Is it a bad idea to get rid of it even if it hideous? If so is there a cheap idea for insulating without framing?

I wouldn't remove it because it's serving a purpose. If it's an unfinished basement, what does it matter if it's ugly? I haven't seen a great looking insulation. If it were me, I wouldn't worry about it, or finish your basement.