I would not see why you need thick cables. If it is a grounded extension cable anything will do.
I haven't done electrical work in a long time now (so, some of my info may be out of date ... I'm old ...), but IIRC, I ran 12Ga for the 15A outlet circuits in the last house and a "standard" grounded extension cord is 18Ga. From my recollection of that round of circuit planning, a freezer will draw 10-14 Amps when the compressor kicks in, which is over the 10A rating of the 18Ga cord.
My numbers may be out of date, but having seen homes destroyed because somebody thought that "anything will do", I would lean towards a nice short 14Ga cord.
Maybe it is "more than you need", but it beats the hell out of the alternative.
And, Ray -- I use a 14Ga cord with my freezer.