Putty is pretty awful anyway. Git for windows installs a shell that is not terrible, includes an ssh client, and is distributed over https. It is my go-to when I have to use a windows machine.
What causes you to say that putty is pretty awful?
Can you seriously compare PuTTY with even the most lacklustre terminal available on OS X or Linux? It's an atrocity of UX design straight out of the Windows 95 era.
Their home page is also the epitome of not caring about user experience even to the slightest degree. Nearly zero effort: http://www.chiark.greenend.org.uk/~sgtatham/putty/
I've seen people construct more impressive pages given only a few hours of HTML and CSS training. I'm not even kidding.
I'm not saying everything has to be slick and beautiful, but there's a thing called pride in craftsmanship, and PuTTY has none of that. It's just sad.