at this time of year 和 at this time of the year 都正确。例如:time of year, time of the year 一年中的 ... 时候 The leaves start to turn red at this time of (the) year . 树叶在一年中的这个时候开始变红。(摘自《牛津英语搭配词典》第二版p.1827)
2. this time of year, 还有 this time of day,this time of night 等,of 后面的名词省略冠词,是因为把 this time of 视为“词组限定语”对待,类似 this kind of car 的用法,把this kind of 看作限定语,car 之前不加冠词。