What is the ideal number of farms and wine fields?

I believe your question is about optimal field count, not a maximum one ;)

The number can be checked quite easily by making a test map with only a Store, Inn and a Farm/Winefarm. Start the game and wait till production begins/stabilizes, then make a sample for a 5-10 minutes, by counting corn/wine in the Store. Repeat the sample for different number of fields.

Vanilla game answer:

• Farm - 15-16 fields
• Wineyard - ~12 fields

KaM Remake:

• Farm - 15-16 fields
• Wineyard - 8-9 fields (wine was buffed to make it more competitive strategy)

Note that making a giant field between several farms will generally lower your corn/wine production because farmers will stumble into one another from time to time, when going to cut/sow/collect their crops.

I'm playing this game again since recently, and i find that a farm does not need more than 12 fields to keep his farmer occupied. Because that's all that is to optimal field count. Your need just enough fields to keep your farmer busy, make sure he's not idling around in his house. for that i usually do 14-15 wineyard tiles, and 12 wheat tiles.