in case of this, I guess you still end up with two queries, so there is no point in that.

$products = Category::with('product')->find($category->id);

To get only one picture query should look smth like this, though I did not test this:)

Product::with(['picture' => function($query){
    $query->take(1);
}])->get();

Limit on eager loading query for a SINGLE model just like @luknei said, but to clarify, if you use such statement for more than just one model like in the example:

Product::with(['picture' => function($query){
    $query->take(1);
}])->get();

then you will end up with only one related picture (in total, not one per Product), as it's going to use LIMIT 1 on the query.

Now, this part:

$products = Category::with('product')->find($category->id);

is not going to return products, but category with appended related products.

So for a single category I'd suggest using this code:

$category = Category::find($category_id);
$product = $category->products()->first();

This way you have exactly the same number of queries and it's much more clean.