Personally I wouldn't bother fitting tyre's just for this trip,
When you can get a set of snow chains
( That fit in minutes )
for under £30, I particularly like this type
Temporary fitting these to the front wheels,
makesALL the difference
when your draging yourself ( plus heavy caravan ) out of a muddy field
Example:: see here:: https%3A%2F%2Fwww.ebay.co.uk%2Fulk%2Fitm%2F152558285392