I understand the meaning of the sentence, but I have difficulties grasping the pattern and how I could extend it to other phrases. Could you please come up with other example sentences with similar patterns?
You can also say 一年有四季：春夏秋冬 which has the same meaning. As @stan has said, one of 四季 or 春夏秋冬 is an appositive word. In general, the word as 四季 is put later since it has a function to summerize or explain the words before it. BTW, sometimes, 有 will be canceled, i.e. 一年四季，春夏秋冬. There is a poetry Chinese children will learn:一去二三里，烟村四五家，亭台六七座，八九十枝花, 一去 and 烟村 and 亭台 has the same function as 春夏秋冬 in your example while 二三里 and 四五家 and 六七座 has the same function as 四季.
In it's most basic form the pattern should be:
subject + verb + (quantity) object
e.g. 一只猫 + 有 + (四条)腿 <-- (brackets not necessary, just trying to make the distinction clear)
一年 + 有 + 四季
In your example the sentence is expanded to list out what each of those items in the object are:
The 四季 includes 春、夏、秋、冬.
So the sentence pattern then becomes something like:
subject + verb + list of objects + (quantity) object
一年 + 有 + 春、夏、秋、冬 + 四季
Here is another example of the same pattern:
我的家 + 有 + 爸爸 妈妈 和 我 + 三个人 (我的家有爸爸妈妈和我三个人)
Additionally, one of the first sentences I learnt from a text book was:
Which is similar to the pattern above, but you can see the place of the number of objects (四口人) is switched with the list of objects. Both ways are acceptable.
I suppose this is a pattern that is to describe a subject, which can be interpreted by different terms, but you can combine them together as a whole, so as to explain it more dramatically.
For the sentence you give, you can say a year has 4 seasons, and a year has spring/summer/autumn/winter. Then you can combine them together a year has spring/summer/autumn/winter 4 seasons.
Another example is
"空间有上下左右前后六个方位" - The space has up/down/let/right/front/back 6 directions.