Yeppers.
The last couple of campaigns I ran I kept track of weather, dates, holidays, time, the calendar, etc. In the last campaign in particular, it was extremely helpful as the party was adventuring further north. So, when it started into Fall, they knew that their campaigning season was drawing short. Winter was harsh enough that the party, and most everyone else, just hunkered down, and resumed their campaigning come spring.
Having a calendar made things much easier too when quests came along that required someone to find something within 101 days. And too, when you have armies on the move, to figure out when they would get somewhere as opposed to when the PCs would get there.
Not only did I keep track of those elements, but keeping notes on what the PCs did helped immensely too. They, and I, could look back over those notes, and in relation to time, see where they were with their own goals - or even if they missed something. It was sorta like a calenderical scribe.
Tool wise, I kept track of everything, including notes, with a Campaign Calendar application that I'd written in Visual Basic 6. With the user interface the players and everyone could see the current month and what was the current day and approximate time, as well as any upcoming events and any past events. (My calendar had 10 months, each month with 4 weeks of 10 days each, each week having 7 work days and 3 weekend days, with the full moon happening the middle of each month, with three months of winter and summer, and two months of spring and fall). I even could export the calendar to HTML files so that they could be posted on the campaign website.
Weather though, was done on the fly for the most part - keeping with the season and timeframe. That was the only part I never really handled with a tool.
I'm hoping to be running a Pathfinder campaign eventually, so I am in the process of doing a complete overhaul of the app to .NET (and using XML data files vice an MS Access DB).