Hi There
I'm a Canadian so your Colorado winters are pretty similar to what we have. I've been to Portugal several times in the Jan/Feb time horizon. Anything they can throw at you bad weather-wise is going to be better than what you'll have at home. Remember that old chestnut "at least you don't have to shovel rain"!
Last winter when I was in Lisbon in January it pretty much rained the whole time. And I had a totally marvelous time. My photographs are some of the best I've taken: the colours are so much richer in that kind of lighting. Make certain you travel with layers of clothing so that you can adjust as the weather changes. Because when the sun does come out it becomes very warm, very quickly.
Like a few other folks I wouldn't recommend traveling into the North during the winter because it does get colder and damper as you move north. But keep in mind it isn't the kind of cold you'll have at home. It's all relative.
The Algarve will always have much more sun, regardless of the time of year. But even last winter they had an incredible amount of rain (probably the wettest winter on record for 30 years!) In these times of climate change, I think all of us travelers have to be prepared for 'non typical' weather patterns unfolding. One of my clients went to the Algarve in February on her first trip to Portugal. I was concerned that she might not have had a good time because of how cool and wet it was. But she's reported that she had a fantastic time and can't wait to go back.
On the topic of public transportation, I too would recommend hiring a car once you are ready to leave Lisbon. Keep in mind that once you're outside the larger centres, Portugal is a very rural country. Many of communities in the hills and along the ocean are fairly isolated. People either drive or are content with infrequent local bus service. In American terms, it would be like being in Phoenix and deciding to head out to Sedona for a short trip. Sure you could do it by bus (train I'm not sure of) but it would take you a fair bit of time and coordination. Much easier to have a car.
The good news for us North Americans is that they drive on the same side (the right side, many would say :)) as we do. Most of the rules of the road are the same. The big challenge is that, like the rest of Europe, Portugal uses a lot of traffic circles. But frankly, once you've been through one or two they actually become fun. I find myself wondering why we don't have more of them because they keep traffic flowing so much more smoothly. One other factor about European car rentals is that pretty much everyone drives a standard (manual) transmission. You can certainly rent an automatic, but be prepared to pay a sizeable upgrade fee.
My favourite Portuguese owned and operated car rental company is Amoita (www.amoita.com). Last winter they happily brought a car to my hotel, held an umbrella over me as I put my luggage away in a downpour, gave me good directions to the nearest highway entrance and then let me drop my car off at the Faro airport with no additional drop-off fee. Now that's service in my books.
Because you are traveling in low season, if you are open to it, you might find that traveling with a good guide book and a light schedule is your best bet. Very few hotels will be full so it likely won't be difficult to find accommodation as you move along. I've found that despite its tiny size, Portugal is chock-a-block full of delightful little corners that invite you to stay a bit longer. Too many times I've had to rip myself away from a place and its people because I was scheduled to be somewhere else. Those trips where I've been able to ramble at my own pace have been the best. I typically don't get as far as I'd fantasized before I left home, but I've had a better, richer experience of the shorter distances once I arrived.