Морозная -is frosty холодная - cold Despite what you mean. If you want to say that the winters are cold, it is said Холодная зима and if you want to say that the winter was frosty say Морозная зима

Морозная ( погода, зима) - it is when frost weather stands . Frost-it is when temperature 30 and lower below zero . Холодная ( погода ) that word is mostly used then temperature is lower then usual one . It can be in summer , when temperature is 15 above zero , it can be in winter then it is 25 degrees below zero . also we can say - холодная одежда ( dress does not save warm ) холодная комната ( it is cold there) холодное отношение ( not so good attention ) . But we never use word морозный at that point

Морозная зима - it is when temperature often is lower then 30 below zero- Холодная зима - it can be used in the same case , but perhaps it word does not describes frost weather

Морозная зима is more literary language. Холодная зима sounds without "colors"

Холодная зима." Мородная" это , наверное, морозная. Морозная зима тоже может быть.