I think there will be a demand if you are good and reasonably priced, certainly up here in Valais, lots of ex-pats talk about such things, who they use and can trust to do a good job and not get charged massively. There is competition so you'll have to overcome that and the language barriers (if any) and word should spread.
Assuming too that you have (ir can have) all the permits in place that you will need or you don't need them?
There's undoutedly a demand but there is also a lot of gardners already. As for being cheap, by the time you have paid for a van, some power tools, your pension plan, AVS, insurance, salary, even charging Chf 60.-- an hour it will be hard to make ends meet.
A van, fuel, insurance, tax amortisation will cost about 1200-1500 per month, 14.5% AVS, unemployment & family contribution, employers contributrion to Pension fund, 13%.
So with Chf 60.--/hour x 40 x 4 = Chf 9'600.--/month. Minus van, cost of tools (you need professional tools not the ones from the local DIY store), lets say Sfr 1'000.--/month for amortisation, fuel, repair bills, consumables, we already down to Chf 7'000.-- without any other reductions as mentioned or holiday pay or sickness or injury allowances.
You should also take into consideration it's unlikely you'll have 40 hours of regular work each week for at least 1 year.
Chf 60.- is realisticaly speaking a basic minimum, for a professional person.
Chf 40 x 40 x 4 = 6'400.--brutto minus social costs, pension fund contributions, accident insurance (note accident covered by employer and not medical covered by yourself) tools, equipment, fuel, running costs, maintainence, amortisiation, consumables.......... would be very difficult to have more than 4k netto, assuming you work 40 hours each and every 52 weeks of the year.....from day 1 of course
Sorry if I am stating the obvious. More snow here then the UK. I could be wrong but I guess if everything is covered in snow, then gardening it... difficult.