There's one thing that fully wakes me up every morning better than a dozen cups of coffee ever would: biking to work.
That would be a combination of not being addicted to caffeine (so you are not in need of a fix) and the better REM sleep you had prior to waking up.
In my opinion!
I'm from Sweden, and when I lived in Gothenburg I had no issues biking in -10 - -20C or so (which is what it maxes out at in that area, and even then only for a few weeks at most).
Snow is fine to go on - the worst is like 0C when its been melting and freezing so you get slippery ice, but even then you do fine most of the time as at least the car parts of the roads tend to be maintained with gravel. Assuming you live somewhere that regularly has cold weather your roads are most likely decently graveled too.
Sure, if you live in Moscow/Anchorage/Montreal/Stockholm/etc, it's miserable for a few months, but the rest of the time, you can cycle.
Plus, cycling in the cold wakes you up even faster than cycling in the heat.
They have the crazy huge tires as well to go over snow/ice. Each one said its not a huge deal to bike in -20ish weather with snow/ice. Just means you travel slower was their statement.
As for the shower, some work places have showers. Depending on how much you work out and what the climate is like you may or may not be a heavy sweater after a ride to work. People who work out often tend to sweat more because their bodies adapt to their routines and start to sweat at the slightest hint of physical exercise. People who don't work out extensively often tend to be more reserved when it comes to sweating. You are going to work, not a date. So it may not be an issue at all.
I can't wait to get a bike next season and start biking to work.
Then a couple of years ago I went on a bike tour, so I upgraded my bike and got some actual panniers to store stuff.
The change was amazing! Not only can you carry more, but you also avoid the strain and sweatiness of having a backpack.
yes also to OP on the "bicycling to work wakes me up super well" - i did in a northern US city for 6 years, and the icy/cold months when i had to rely on transit instead were remarkably more challenging, especially the mornings, even if i kept up other indoor exercise.
FWIW chalk improves the friction coefficient of your hands, and seems to reduce friction damage to the skin, so I try to use it anyway.
Sweat. If you have a shower at work then great. If not there's no reason to go full tilt on the way to work. Relax, go at a reasonable pace to avoid working up a major sweat. We have a shower at the office, but I rarely use it because it's not too hectic of a ride.
Store stuff at work. Drive into work on a Monday and bring clothes and stuff with you and store in a locker or somewhere at work. Then bike the rest of the days and drive home later in the week.
If you can leave your laptop at work the odd day.. you'll enjoy life at home that much more :)
Luckily for me, my office provides showers and lockers, a laptop I can keep at home, and free lunch on the premises, so load is not much of an issue for me.
If you do need to carry some stuff, you can always get a pannier(a bag mounted to the side of your rear wheel), which is more comfortable than a bookbag filled with stuff.
I've gotten lazy and haven't biked in in awhile, but I used to do it every day by heading into work about 30-45 minutes earlier than I would drive, swapping my shower immediately after I got up for showering at work, and compensating for a slightly longer commute. If you compare the amount of time you'd spend driving to a gym, working out, then driving somewhere else, it's a no-brainer, bike commuting kills two birds with one stone and saves you gas money. Or you can try what I did for a while and get up even earlier to bike to the gym, workout, shower, then bike to work, using the cycling as warmup and cool down for the gym workout.