It depends on lines of latitudes on both hemispheres. The northern hemisphere may appear to have colder winters that us in the southern hemisphere but that may be because a large of part of the Earth's landmass is in the northern hemisphere.
For example the 60 degree north latitude cuts through southern Alaska, about mid Canada, southern tip of Greenland, Sweden, Norway and about approximately mid Russia.
Same latitude in the south, cut though nothing but ocean.
Southern tip of South Africa is at 33 degrees south (comparable to north Mexico),
while New Zealand and Australia (including Tasmania) are roughly 46 degrees and 44 degrees south, respectively.
Comparable to northern states of USA or south of France.
Southern tip of South America is roughly 56 degrees south (same latitude as UK, Canada, Denmark in the northern hemisphere)
Basically, the majority of comparable latitudes in the northern hemisphere are covered by land while in the southern hemisphere, it's mostly ocean.
To answer your question, it's neither yes nor no because of the reasons listed above.