Is 怡养 in this sentence a word？ Is 怡养 a word？
Is it one of these meanings?

和乐。
犹保养，休养。
犹陶冶。

怡：和悦，愉快：affable, cheerful
I thought it might be related to: 颐养天年, but that is a different yi.
How would you translate:
书法学习是一件怡养身心的事，可以给人带来无穷的乐趣。
书法学习是一件怡养身心的事，可以给人带来无穷的乐趣。
Studying calligraphy can nurture/nourish both body and mind, and can bring endless pleasure.

頤養/颐养 and 怡养 are both valid words, but their meanings are slightly different.
颐养：
Wiktionary defines 颐养 as

(literary) to maintain one's health; to keep fit

And 《现代汉语词典》（第七版）defines it as

〈书〉保养：颐养天年。 | (literary) to maintain (one's health). e.g. 颐养天年

怡养：
Neither Wiktionary nor 《现代汉语词典》includes this word, but it does exist. According to this page, it emerged as far back as 200 AD. It means:


和乐。

《文选·嵇康＜琴赋＞》：“若和平者听之，则怡养悦悆，淑穆玄真。” 李善 注引《广雅》：“养，乐也。”

犹保养，休养。

南朝 梁 何逊 《入西塞示南府同僚》诗：“情游乃落魄，得性随怡养。”《旧唐书·丘和传》：“ 和时年已衰老，乃拜稷州刺史，以是本乡，令自怡养。” 宋 林逋 《山阁偶书》诗：“餘生多病期怡养，聊此栖迟一避喧。”

犹陶冶。

茅盾 《官舱里》：“‘哦，丝竹是能够怡养性子的。极好，极好！’老先生也郑重地赞叹着。”

which is probably where you find your explanation, or where it comes from.
But please note that the chance that you see the word used to mean the first sense listed (&quot;和乐&quot;) in modern days, even in written form, is infinitesimal. It's a very archaic usage; the author of the prose containing the example sentence was 嵇康, who lived in 三国时期 (the era of Three Kingdoms). As you can see, the expression already required a footnote to explain it in Tang Dynasty, when 李善 lived.
In its second sense, it's the same as 颐养.
Its third sense is the sense that's used in your example: 陶冶, meaning &quot;to cultivate; to train; to mould someone's character&quot; (Wiktionary). The example sentence came from a modern writer.

From my own experience, both words, 怡养 and 颐养, are still somewhat common in written Chinese, but less used colloquially. Both words are literary and very unproductive when forming phrases, especially 颐养, which you'll almost only encounter in the words 頤養天年/颐养天年 and 頤養精神/颐养精神, or some variants of the latter, unless the author's writing style calls for it.
Also, some four-character phrases are in the form of 怡/颐A养B. e.g. 怡情养性, 颐神养性(variants 颐神养气, 颐神养寿). Some of them can sometimes be seen in the form of 颐养AB, e.g. 颐养神性, but less often.