Gosh reading these replies shows me why so many people don't want to take a risk to work for themselves.
Yes OP it is viable.
Near me in a small village a horsebox coffee stall opened up at the beginning of lockdown. They are on a farm, there's some haybales for seating. So on private land presumably paying something to the farm. They are busy with wakers, cyclists and people wfm.
Whilst on holiday this year in the UK I saw coffee shops on the back of apes (italian motorbike trailer thing not gorillas) pitched up near beaches in car parks.
Its all down to location.
I would concentrate on coffee. You run the risk of being all things to all people. Doing ice cream and alcohol will increase your costs ie you need coffee machine and refrigeration and heating equipment.
Ice cream vans are all owned and run by what I can best describe as cartels. Some sort of mafia operations. Have a look in your area if this is the case. Same for hotdog and peanut stands in London, I gather its all cut throat.
Talk to your local council. Talk to lots of people. Ask for help. There will be people really keen on your idea who will help put you touch with owners of land you can use to pitch up. I think this is better tha driving around the streets.
Also think about what hours of the day you want to work. Coffee is early morning into mid afternoon, ice creams afternoon into early evening, mulled wine is also later in the day. You'll never get any time off trying to cover all of those. Coffee on it's own has a good window of time and then take the late afternoon evening off (to do paperwork)
I work for myself, a business with huge overheads, don't let that put you off.