Bagel Failure - what happened?
It sounds like your yeast never really got started, and you may have killed most of it off. Sugar actually retards yeast, and salt kills it, so mixing sugar and salt into the water was not a good thing, in fact it didn't kill off the yeast completely it probably did most of it. So you started off with very little live yeast, which has knock on effects. Cold conditions make proofing much slower, and what yeast you had wasn't enough to make things rise.

Yeast can come back in some cases, providing there's at least some in there, you just have to give it time to reproduce. I've had bread take 3 hours to really get going when I've had old yeast or mistreated it, and the results were fine in the end. If I suspect I've killed my yeast I've had some success kneading more in with a bit of water, again giving it more time. 

The message here is not to go for a time, but a result. If you expect a dough to double in size or more then don't move on to the next stage until it does. Home bread baking is not an exact science, so be prepared for things to move faster or slower. 

A couple of things about bagels:


Bagels won't rise or expand much in the oven as boiling them cooks them, fixing their structure. If they aren't risen enough before boiling leave them be until they are, there's no oven spring! 
Bagel dough is supposed to be dense, but you can overdo it. Don't add any more flour than the recipe calls for
You can over-knead any bread, but 15 minutes doesn't sound like too much to me


I've found that using a sponge is very good for getting consistent results, in fact I won't bake yeast breads without one anymore. A sponge is a 50-50 mix of some of the flour and water from your recipe plus all your yeast which is then set aside covered. This gives your yeast an ideal environment to get started, once it's really happy (generally 30-45 minutes) you then add the rest of the ingredients (salt last) and proceed as normal. If your yeast is dead you will know it within 15-20 minutes or so and you can start again, otherwise you wait until it's super bubbly. A sponge also adds flavor I find.