if you can take your starter out, then you can check if oil's getting on the plugs.....just pull a wire and if there's oil in the spark plug tube then you need valve cover gasket with the tube seals...but honestly...it sounds like you just need a battery. especially with the cold weather, your alternator sounds like it's charging the battery, but it sounds like the battery's not holding sufficient charge to give enough amps for cold starts. it sounds like the timing is fine also, when you did the timing belt, did you do the water pump? cam + crank seals? balance shaft oil seal? and most importantly the balance shaft oil seal retainer? it's a little $5 2 bolt hole metal bracket that keeps that balance shaft oil seal from blowing out and leaking like a mofo, you can get em from honda for like $5. if you've had that battery 3 years or more i'd definately put a new ( not crap ) battery in there and go from there.