My first question to you would be: do you eat anything before you ride - either way? My commute is 6 miles each way with the ride home involving a climb back up the mountain.
When I first started commuting I did what you did: I rode Tues and Thurs for the first few weeks, then went to Mon, Wed, Fri for a few weeks etc etc until I was commuting every day. What I did find was I needed to eat something about 20 mins before I started my commute home or I would just wear out on the last big push to home. I also try to eat my dinner within the 1/2 hour window after getting home: due to the climb I have to make it seems to help. Since your commute involves hills - try elevating your legs for a while in the evenings when you ride. Sooner seems to be better than later but I've elevated my legs as much as 3 hours after I got home and seemed to feel some benefit from it. (don't ask me what...could be all mental - actually knowing me it probably IS all mental!
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As for the cold - I find that starting out cold for a commute is the worse possible way to commute - the ride isn't long enough or hard enough to get me warm by the time I get to work so I end up cold all day!
You might look into rainpants as you suggested: make sure they are wind and water resistent if not proof, it helps to keep the ugly stuff out and keep the warmth in. For my commute this morning it was 21 degrees with a wind chill of 11. The last 2 miles of my ride involved riding in a head wind. My riding outfit was:
Winter Weight UnderArmour, Lightweight Long Underwear, Jersey and Wind Jacket on top
Fleece Leg Warmers, SHorts, Tights, and Rain Pants on the bottoms.
Polypro underliners, mid-weight cycling gloves and overgloves on my hands
SmartWools and REI rainsocks on my feet with toe covers.
I made it to work with very little frozen stiff and the nice thing about layers is I can pack some of them away for the ride home since it's "supposed" to be warmer! (yarite) or change the layers around each commute to fit the weather. Several ppl here will suggest other things they use including plastic bags on their feet, sweatpants, fleece pants - etc. You might have to play around with some combos to find what works best for you but don't give it up......commuting to work makes Such a huge difference in your day!!
My winter commutes are always slower and some days it feels like my muscles never get warmed up - on those days I just ride for the beauty of nature and don't worry about how long it takes me. and remind myself that I only have 3 more months of this and riding in the winter keeps me in condition for spring And riding in all those clothes on a heavier bike might actually Improve my conditioning for spring! (ahhh the these we tell ourselve to motivate us!
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and DRINK DRINK DRINK - a lot of ppl forget to drink in the winter coz it's cold and they don't feel thirsty but you need water just as much in the winter as you do in the summer. My evening commute takes me 30-40 minutes depending on the wind and if my water bottle isn't at Least half empty by the time I get home, I make myself drink a huge glass or 2 of water right away.
Hope this all helps and yes: if you get a chance check out the "getting to know you" thread under open and learn even more about us....and tell us something about you!!
and Good Luck and Have Fun!
PS: Lights...don't forget headlights, reflectors and reflector strips, blinkies - whatever it takes to make sure you can see and be seen!!
Life should NOT be a journey to the grave with the intention of arriving safely in an attractive and well preserved body, but rather to skid in sideways, champagne in one hand, strawberries in the other, body thoroughly used up, totally worn out and screaming: "Yeah Baby! What a Ride!"