I would recomend small wheels if you have them and tyres with good tred.
Chineese cheepos tyres ftw but as Al mentioned even if you have good tyres on they will not wear badly as it will be wet.
Tyres with no tred is potentionaly going to end your day quickly and waste your money. I would describe no tred as being on the indicator ie 3mm tred left.
As I said 3mm may get you through but is an unnessary risk.