Of course, I will thaw in advance and pre-incubate for a period of time, but I am not sure whether the temperature stored at minus 80 degrees will affect the experiment?
I think that you could do some basic drying-rewetting experiments on soil cores that have been frozen at -80°C, but you will need to be careful about your expectations and the caveats you will need to state.
It is most likely that the freeze-thawing process will differentially kill microbes already present in your soil cores. Depending on your post-thaw incubation conditions, some microbes may recover, grow and produce compounds which may effect the following drying-rewetting experiments.
If your soil cores initially had a high water content, humus and clays, the thawing might result in significant changes in core pore structure, especially at the micro-metre scale. This in turn might effect the drying-rewetting experiments.
If you have enough soil cores to play with, you could see what the drying-rewetting characteristics are like (you could measure the water content / matrix potential, or total weight of water uptake, and then look at the drying profile over time at a set temperature), and use replicate cores to produce you own, new, packed sieved-soil aggregate cores (i.e. thaw them, sieve them to 2-3 mm or whatever is appropriate, and then repack them to the original soil density). (You would also need to decide whether it is better to sterilise the soil or use it as it is.)
We have previously looked at packed double-autoclaved sieved-soli aggregates as part of some work to establish whether bacterially-produced surfactants effect water distributions in partially-saturated soil pore networks. This was rather fun to do as it is not normally what we do, but it is important to do the soil biophysical measurements properly and in a way that the soil biophysics community expects (rather than what a microbiologist, such as myself, might think is reasonable).