Fresh cider and pressed juice is routinely frozen without major degradation. It is not quite as good as fresh, but no major deterioration. However freeze it well, I would recommend 10F as the highest freeze temperature and would prefer lower, and limit how long you freeze it for as it will slowly deteriorate. Frost free freezers will typically deteriorate faster because of dehydration. A well sealed container will help, many people do not seal until the contents are frozen to avoid possible rupture from expanding liquid. Always remember to leave adequate head space for expansion during freezing.
When you thaw, remember to mix as some separation is likely to occur. Thawed juices with have a tendency to turn or start to ferment faster than the fresh juice. Also, freezing never completely arrests deterioration, it only slows it, so the longer the juice is frozen, the lower the quality will be when thawed. Peak of season juice a few months later will still often be superior to fresh pressed from inferior produce though.
Fresh fruits and vegetables tend to often thaw soft, mushy, and almost bruised tasting after thawed because freezing and thawing tends to break down the cell structure. Pressed juice has no such issue as that is exactly what you are doing in the juicing, breaking the cell structure and extracting the juice.