N’t I plant trees in Winter

TLDR: I find micromanaging my foresters outside of an emergency to be entirely unnecessary. If you're having trouble keeping up with logs or firewood, you should reexamine your town's layout, the availability of general laborers, and the condition of your workers.

Long Answer:

As nickson104 says, there is some usual advice to give some forester huts orders to "plant only" to maximize the harvest of the herbalists & gatherers with which they are grouped. In my experience this is an optimization in search of a problem. Once my food industry is in full swing, any drop in production from my gatherers will be more than compensated for by my farmers. And with any reasonable building/firewood demands, production of food and herbs will not noticeably suffer. In addition, with a well rounded diet available, herb consumption can drop to well under a dozen per year for each hundred people.

Now if you do find your town stressed for logs, which is more likely to happen in winter, two solutions present themselves.

1. "Cut only" orders (as you ask about) for the forester's huts near your woodcutter's stockpiles will focus the minds of your foresters on producing logs without damaging younger trees. This produces a modest up-tick in short term production, without damaging long term production (provided you remember to start them planting again afterward).
2. Clear cutting by laborers (as nickson104 suggests) is fast. Unfortunately you will also fell saplings for no short term gain and a long term loss. Fortunately educated laborers don't need to clear cut a very large area to avert a firewood emergency.

Remember, if you're trying to accelerate your Firewood production, these things need to happen near the woodcutter's stockpiles. If they are forced to regularly march to a distant stockpile for logs, this will just slow them down. To optimize firewood production, I'll often put a large (10x5) stockpile directly outside my forest cluster with my woodcutter just across the street from it. While I find the starting log quota of 200 suits me for much of the game, I will often bump the Firewood quota by an extra 1000 when I either start trading in firewood (the buffer for large trades is invaluable) or when I start mining/trading for coal (having the markets carrying far more firewood than coal means that's what the people generally will use as fuel. That coal is for tools gosh-darn-it!)

Lastly, why are we in this predicament in the 1st place?

• Are your Foresters or Woodcutter walking too far to get to their shared stockpile? Make sure there's a sizable stockpile directly between your woodcutter and the working border of your forest cluster. Beware of putting additional stockpiles too close to the forest cluster. Foresters may drop off logs there for a small savings in their time but forcing the woodcutter to walk across the cluster to grab them. Markets are a poor alternative to a shared stockpile as they stock a limited number logs, more than enough for a blacksmith, but not a woodcutter. The woodcutter will collect, ideally, 9 logs at the start of his relatively short work cycle. At the start of his next cycle the market will be unlikely to have restocked the logs, so off the woodcutter goes to the stockpile. Congratulations! You're potentially using the better part of 1 Vendor's time to hopefully halve your woodworker's walking penalty for your poor town planning. In the end make sure that Foresters/Laborers are bringing the logs to the Woodcutter. Let Vendors worry about the firewood after it's cut. They're very good at that.
• Do 2 or more Foresters' buildings have overlapping work areas? Overlapping the work areas of similar buildings seems to trash productivity.
• Are your foresters or laborers uneducated? The uneducated will get one fewer log from each felled tree. Don't skimp on education!
• Are you trading exclusively with firewood?
  1. You'd better have a large firewood quota to deal with your traders' demand spikes without depriving your homes of heat. I keep 625 Firewood in my Trading post to cover the costs of new seeds. My woodcutter's quota will be more than enough replace that 625 after a trade or two and still heat the town. (Did I mention I give my woodcutter a large stockpile?) If your stockpiled firewood is not enough to safely allow restocking your trader, perhaps you should reconsider the trade. Worst case scenario, you can always dump your Trading Post's supply of firewood back out into your town.
  2. Diversify your exports:
     • What's the one class of items going into your barns that you can't put a quota on? Animal by-products! Chicken and Sheep along with Cow & Dear Carcasses have absolutely no respect for your well considered quotas. Your people will eat the eggs, but make sure your barns are not filling up with wool & leather. Once I get sheep, I'll build a 2nd tailor shop. Warm coats for my people & wool coats for the traders. Before that, spare hide coats can be traded.
     • What Food item do you produce better than any other? Take this opportunity to balance out your food supply. Like any firewood you keep in your trading post, the ability to release stock back to the town can also be a hedge against lean years.
     • Keep a handful of eggs and fish in your trading post. They sell for 1 or 2 each. Don't let your guest "keep the change."
• Are you trying to heat too many wooden houses? Upgrade to stone houses to reduce your need for fuel. Build a quarry & hire a stone-cutter. Better yet trade for stone/iron/coal.
• Do you have enough happy and healthy laborers living relatively close to the woodcutter? If a laborer finds himself free while near the woodcutter he may help clear the woodcutter's yard, leaving the woodcutter more time to actually cut wood.
• Have you ordered an unsupportable building boom? Pause construction. I've found that, after surviving your 1st year and then getting your tool/clothing/education supplies locked down, patience is your friend in banished.