It should vary based on the themes of the adventure. Frolicking in the Shire should incur basically no Shadow, while going to Mordor should be drenched in it.BTW, how do you use Shadow Points? Is there any recommendation on how much shadow players could be exposed to per adventure? Like 3-5 shadow points?
I agree with Harlath that you should account for how "old" the characters are. It's not fun being hit by Shadow when there's nothing you can really do about it because your Valour/Wisdom is so low. I know that there are GMs that groan that they don't get their blood in the form of bouts...but what's fun for the GM in punishing characters isn't necessarily fun for the player.
I wouldn't say no Shadow, but keep it limited and controlled. You can be more liberal with it once they stand a chance of beating the Shadow Tests. Bear on mind that players usually get to remove Shadow at the end of each adventure. How much you should give depends on the player and how much they enjoy it. My wife hates it, so I give her very little Shadow (we play with just us two so I can afford to tailor it to her like that). Others love it. I personally like enough to feel like it's something to be aware of, but low enough that I can manage it. Look to your players and see how they enjoy it.
I'd say that about 3 or 4 Shadow Points per session on average works well. That's on average though - I will go a session or two without any or only one or two, then the final one before Yule is often a capstone one and that might have ten. It gives it a nice meaty and gritty feeling...without constantly soaking them in Shadow.