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