At higher levels I think it definitely pays to try and keep at least 2 forests in your cities AT THE BEGINNING of the game. The point about how 2 forested grasslands can be turned into a farm (negating the -1F) and a cottage, plus the hammers for chopping, leaves out the HUGE point that you are then REQUIRED to work the farm (to break even). At higher difficulties, the trade off is more like this one:
You have a city with pop 3, not on fresh water. Your health is as follows: +1 from fish, +1 for difficulty, +1 for forests (assuming you have 2 left). The disease is -3 from pop, so you are maxed out heathwise.
Your fat cross contains a pastured horse tile giving you 1F 4H and 1G. You have plantationed silk giving you 2F 0H and 6G. You have a cottaged floodplain giving you 3F and 4G. These three tiles give you 6F, 4H, and 11G, at break even (no growth) with the two forests. If you chop, then farm grass for extra food, then you have to take citizen off of one of these tiles to break even. If you remove from silk and put on grass farm (next to river) you are left with 7F (same as 6F w/ forests), 4H, and 6G (i.e. -5G per turn). If you take horse citizen and put him on a plains river farm, for example, you get 7F (even), 1H, and 11G (i.e. -3H per turn).
I am just saying that keeping a couple forests (if possible, i.e. not chopping for serious war, or courthouse or aquaduct, and even in some cases if they are options) ALLOWS you to work a larger choice of tiles. When the number of tiles that can be worked is small (beginning of game, size 3-5 cities), and there are several resources in your fat cross, the trade off of unworking a "resourced" tile for a mere grass farm tile, can be a fairly substantial negative for sure (and far from an "even" deal + chop hammers)
That said, after aquaducts, or if I have plenty of health resources, I chop em all. But very very early I often keep a couple for the +1 health on high difficulties.