Some context: in 2011 I was on a trip in Vermont when Hurricane Irene (or more precisely its leavings) blew through and it rained about a foot over forty hours. Last year I was touring on the Oregon coast in early October when an atmospheric river hit. Both of these events led to a major change of plans.
There are some things you just can't control with heavy weather. One of them is that if it rains a lot, it inevitably begins to flood. That may block your route and force a big rethink of your plans. The other thing is that in such poor weather, motor vehicles have an even harder time seeing you and a cyclist is likely to be even more unsafe than they normally are. So you need to be extra aware, especially in situations with poor shoulders and poor sight lines.
Having said all that, if you are going to play outdoors sometimes it is sometimes wet outdoors and sometimes you will get a bit soggy. If you have a positive attitude, a sense of humor, some tolerance for discomfort, and patience with yourself that can get you a long way and you can still have a great time.
If I can mostly dry out at the end of the days ride I will usually be okay to go the next morning into the teeth of it again. So for me that means I am a lot more likely to try to sleep indoors during extended periods of poor weather, rather than camp each night.
You will be rewarded massively in poor weather if you can keep your gear well-organized. No matter how waterproof your panniers and other bike bags are, they are much less waterproof when you have to open them up and dig through them during a downpour. And no matter how waterproof your panniers are the stuff in them will get just as wet if you put wet stuff in them. So I try very hard to have some panniers and bags (especially on the drive side) that I only get into at camp at the end of the day. Ideally it is only one of the non-drive-side bags that has layers and emergency items and the front bag that has lunch and my phone and wallet that I get into during the day's ride. Also, I carry a small mesh stuff sack and fill it with wet stuff and strap it to the top of the rear rack rather than put that wet stuff back into a pannier. At least in theory that wet stuff can sort of dry out, or at least drain, if the weather breaks temporarily.
Like others, I am not super impressed with outdoor clothing technology that is supposed to keep us dry. To be fair, it is a tall order to keep someone who is exercising hard (like riding a loaded bike up a long hill) reasonably dry in very foul weather.
In temperatures described by the OP, I'd probably be wearing very thin synthetic base layers (they absorb very little water, much less than merino wool), some plausible rain parka (see below), thin base layers or tights on my legs, and perhaps waterproof socks and gloves. And maybe a buff under the helmet.
On raingear, one thing to consider is Frogg Toggs. They are ugly, shapeless, and not very durable. But a full set (jacket and pants) are available at Wal-Mart for about $30. And they perform about as well in terms of waterproofness and breathability as gear costing ten times as much. If you are fussy and careful with them they will keep you pretty dry in appalling conditions. I dislike rain pants and figure that my legs are pretty waterproof and will function okay even when wet.
While not strictly speaking "raingear", lightweight wind shells and pants provide very good insulation for their weight, absorb very little water, and dry out very quickly. I always carry them on a trip.
I like the Showers Pass waterproof gloves and socks and they work for me. Also there are many low-cost (around $15) neoprene booties on Amazon that will keep your feet warm, if not dry. You need to be careful with them because if you wear them for multiple days without letting your feet air out you will risk trench foot. Sometimes I remove the insoles in my shoes to make room for the booties.
In foul weather, I'd expect to maintain a slower pace and keep the stove and cookpot handy to brew up. Also I'd expect to be eating more and would pay more attention to hydration, as it is easy to forget to drink when you are soaking wet.