I found winter commuting very tough on wheel rims, even with daily wiping of the rims and blocks.
Eventually I got a disc braked Giant revolt in 2015 for that reason.
7 miles is not too far at all. Sounds like it might be fun. There's no reason not to try the Carlton a few times to see how you like it, on dry days, but I would certainly agree with the proposal to get something less special for the daily grind. I still ride my best bike to work on dry days.
Give yourself plenty of time the first few times you do it, bear in mind you might want a snack soon after arriving at work.
I'm lucky that there's a shower at work & somewhere safe to lock my bike up.
Otherwise I used to just have a flannel wash in the gents on arrival, which was a while before everyone else turned up.
I would recommend you invest in some thick neoprene BBB overshoes at least, for the winter, if not winter boots. They made a huge difference to my comfort levels.