This is my first year beekeeping. I live in Connecticut and need to prepare my hive for winter. The last two visits I have made to my hive, I have not seen any new eggs. Is this a sign that my queen had died or left ? Do I need to install a new queen, or do I assume she has stopped laying for the winter? Can my bees survive the winter if, in fact, there is no queen ?
I think you need to get an experienced beekeeper to look in your hive. I don't know what your temperatures are in Connecticut, but I supect you are quickly running out of time to do an invasive inspection; although if the hive truly doesn't have a queen, it won't make any difference.
It is too late in the beekeeping year in my area to successfuly install a new queen. I would look to combine the queenless colony with a queen right colony and consider doing a split next year.
It is on the early side for egg rearing to cease completely. If you don't have a queen the hive will not build up in the spring and with no new bees, die out.
Your queen may have cut back due to the oncoming winter. This time of year I dont usually panic if I dont see much brood. My Italians seem to have more than the carnies, and my feral hives have none.. Andrews advice is sound.. if you cant find your queen another set of experienced eyeballs may help...
With only one hive, there isn't much you can do if it is in fact queenless. She may just have shut down for the winter. Maybe... just maybe you will have one more shot to inspect. I hear it's supposed to be in the 50's this weekend. If so, look specifically for the queen.
Next spring look into making a couple of nucs as queen backup.