My group has been handling most months in downtime. Its not uncommon for GMs in any campaign to say "and nothing happens plot related for 3 months. What are you guys doing" Then, over the course of the gametime, I make sure I have events planned that will take up the session and hopefully leave them at a good break. I may run 1-2 turns mid-session, but most months will be handled out of session.
One thing to consider is this is what they plan. You can plan out the month and then go roleplay in the month. I usually handle the building things at the beginning of the month and take it into account for what the players are doing.
What it sounds like to me is you need to get the players to understand that they have to spend time handling the details of running the kingdom. Not all of their time is necessarily theirs to do with as they please.
Trying to match up real time with game time is going to be nearly impossible. I'm just starting VV with my group and we're already 5 years in. I fully expect that we'll go 10+ years by the time we get to the end.
Another thing you can play up as time passes is just how inhospitable the winters are. There are numerous threads here regarding weather in the area and how different DMs have handled it. Basically, it gives you a good excuse to "shut down" adventuring for 3-4 months each year.
What it sounds like to me is you need to get the players to understand that they have to spend time handling the details of running the kingdom. Not all of their time is necessarily theirs to do with as they please.I played up this aspect with a certain encounter using it greatly to his advantage. They made statements to the populace they would spend more time at home and have. I guess I need to plan less encounters and like you said state nothing much happened this month, what do you plan to do.
One thing I do is play up the non-combat/exploration that happens durring those months. Deals they make with various NPC groups, like a mining contract with the Kobolds which takes a week to iron out the exact details. I describe their town, and how it is growing. How the population is exploding as the existence of the gold mine draw in prospectors. Now they have a bunch of unruly people and the marshal has his hands full arresting mooks or making sure they don't get themselves killed prospecting.
Latest, the indroduction of a certain bard made the PCs sit down and focus on making sure their doors were open to citizens so that they could hear complaints, so that his accusations are known to be falling on deaf ears.