A wonderful question, and one that is so drenched in physics that even I, as someone who was once told by his math teacher that he was not allowed to ever take any more math courses again for essentially failing that one so badly, will hazard a shot at it. Of course it should be noted that you should not go off trying to freeze the universe based on any sort of recommendation that I make here. Also, please see the end of this article for a thorough bibliography. And now that we've gotten any semblance of formality out of the way, let's jump right into this question feet first.

As my area of study only gently touched upon physics in my academic days, I felt compelled to consult the Internet for further information. There are a few points that I would like to put out there before we go any further into the actual discussion of your question, however. First of all, I have discovered that the universe has something of a glow about it, not unlike that glow that you have around you after a hearty jog. This glow appears to be residual energy from the Big Bang¹, and this means that the entire universe is quivering at about 3 degrees Kelvin.

So where did this glow come from? Well, if we go back in time from the present to the Big Bang, things get a lot hotter and a lot more compressed. These two things go hand in hand. The Big Bang started everything off with a lot of kinetic energy that flung the universe way open and over time things have slowed down and cooled down to this 3 degrees that we have now.

Now, if we were able to stop everything else in the universe except for us, what would happen? Well the first thing that would happen is that it would get very dark for everyone else, as there would be no more of this 3 degree glow that the universe is currently providing for us. But beyond that, would we continue to rotate? That is to say, would stopping time be like stopping a carousel short? Would we be thrown from our carved wooden horse (that is, the earth) and continue along our path of rotation? I am tempted to say no.

The carousel model does not seem work if you consider time to be "not a dimension but instead absolutely reflective of the rate of change." According Stephen Hicks, an Australian with apparently no physics credentials, if you were to observe the Big Bang when it was occurring from an area of the universe more like ours now, rather than at Big Bang speeds, it would appear that the events taking place in the Big Bang universe were happening at an increased rate of speed. Perhaps like fast forwarding a video tape while you're watching it. Only much hotter. However, life in the Big Bang would just continue along as it always did.

So, if we were to slow down the entire universe around us, we would appear, to the universe, to be moving much faster in our pockets of the universe (disregarding the fact that at Absolute Zero there wouldn't really be anyone else out there to watch, given that, in fact, time was standing still), but we, existing still in our own time, would continue to function normally.

However, I think that another Australian, Baris Purut, has it right when he says "Maybe if we could freeze the whole universe and beyond at zero Kelvin, the dimensional time would really 'stop'! Honestly, I don't really care. I only want to fall in love!"

So I think you have to decide what it is that you really want from life. Do you want to explore the darker reaches of theoretical physics, or do you want to find love? I'll give you some time to think it over.

References:
Time is not the fourth dimension
The fading whimper
Time travel

1. Is the Big Bang a widely accepted theory on how the universe started? I'm assuming yes, since I've not heard anything else lately, and for the sake of argument and research, that's all I found out there. So I'm saying yes. Yes. Big Bang forever! Woah, that's a bit of an oxymoron isn't it?