5 min walk to the bus, one bus stop then hopping on the subway for 20 min, luckily I don't have to change so I can just relax for those 20 min. Then a 10 minute walk to the office.
Not too bad at all for living in a nice suburb of Stockholm.
My impression was that Stockholm is pretty small compared to other capitals, and also well connected with bike lanes. But I visited during summer I don't know about the situation in winter.
You probably need/want winter tires for your bike and it may be cold but sure, it is possible. The bike lanes are usually cleared quickly when it snows.
For me the biking distance would be 14km or so. A bit further than I personally want to bike but not an uncommon biking route.