。
I had a terrible time in the blizzard.
Literal
Blizzard [cause-で] terrible-experience [object-に] encountered.
えらい目に遭う ('to have a terrible experience / to go through hell') is a set phrase: えらい目 ('terrible thing,' where えらい is Kansai-origin emphatic meaning 'awful/terrible') + に遭う ('to encounter'). 吹雪 (ふぶき, 'blizzard') is the cause, marked by で. Short, punchy, and colloquial — the kind of thing someone says after a rough experience.