EB, sorry to hear about your problems. A few suggestions. Winter is a time for a bit heavier kit, some good advice above re Kevlar reinforcing and so on. 23c is a bit narrow for most riding, despite what some people say, a 25c is a bit more comfortable and rolls as easily as narrower tyres. So when change time comes around, think about trying 25c. Look at pressures - for general riding 110psi is a bit high unless you are particularly heavy (and plenty of riding will sort that out!), drop down to 95/100 rear and 90 front. It will make the ride a lot nicer. Lastly, at change time consider latex inner tubes, which do lose pressure more easily but are very supple and will give a nicer ride. They do seem to resist better penetrations as well. Spare tube on every ride, nothing worse than messing about with patches roadside.
When I was a bot younger and competitive, all my training was on tubs, and always with two spares, so now I've got ancient, the habit sticks for my little potters, just two inners in a little package under the saddle. It's like insurance, you carry them about and hopefully nothing happens. Enjoy...welcome to the asylum!