Last spring was a joyful time...

You're mixing up word class and sentence function here. Both these phrases are noun phrases consisting of a pre-modifying adjective (last) and noun (night/spring).

But their function in the two sentences differs. In
Did you see the game on TV last night?
last night has an adverbial function ie it modifies the information in the clause by limiting it to a certain time. It's therefore a time adverbial.

But in
Last spring was a joyous time
last spring functions as the subject of the sentence

I have to say there are other complications which I'm not going to go into because I don't fully understand the logic behind them. But basically :
- think of nouns, adjectives, verbs, adverbs etc as word classes
- think of subject, object, adverbial etc as sentence functions.

Thank you, Sue.

It is now the fall of 2010 and the most recent is the spring of 2010, so is Last spring the spring of 2010?
Is Last spring grammatically correct? Would it be okay to say "The last spring" instead?

Last spring is correct. Without the article "last" and "next" refer to the last/next whatever from the present moment. You only use the article if the reference point is not the present moment. So :

I'm going to Moscow next spring. (The reference point is the present moment, November 2010. So "next spring" = March or April 2011)

I went to New York in the autumn of 1980 and to California the next spring. (ie in 1981. The reference point is not the present moment but 1980)

Thank you, Sue.

Last spring was a joyful time...

Last spring is the spring of 2010, isn't it?

What do you say to refer to the spring of 2009?
"The spring of last year was..."?

Yes and yes 🙂
Or just Last year, spring was...

Thank you, Sue.
Last year, spring was... didn't occur to me. I prefer it.

[IMG]http://www.lusc.jp/lu/item/261282/16866-l1.jpg[/IMG]

That one's a sweetie 🙂