You might consider citrus or other tart fruit with citrus -- mandarin oranges segments are fairly common to pair with spinich; even if you didn't use whole fruit, consider making a vinagrette using orange juice.
I've also seen recipes for spinich salads with strawberries or cranberries; I've also had a pineappe and avocado salad before that might work well with spinish instead of romaine.
Judging by the nutrition information I can easily find (for example, from nutritiondata.self.com), frozen spinach is generally cooked by boiling and draining. That's pretty much what I'd have guessed; it's certainly the easy way to cook things.
Unfortunately, that means that some nutrients are lost with the discarded water. I doubt it'd be different for any other green leafy vegetable - though it's certainly much harder to find frozen mustard greens!
The nutrition information for fresh spinach is for fresh, raw spinach; if you boiled and drained it, you'd make the same sacrifice that the frozen spinach has.
As for your generalization, freezing vegetables and fruits does preserve most things pretty well - but only what's actually left in them when they get frozen! And while transporting fresh vegetables around can cost you some "freshness", it's not going to affect minerals. Some vitamins could be lost by breaking down (I'm not an expert here, but it seems possible) since they're more complex molecules, but minerals are just single elements. Those iron atoms won't fall out of the spinach on the way, and they're certainly not going to be transmuted, either!
Edit: Essentially what's been said in the comments is that the USDA nutrition facts say that "Spinach, frozen, chopped or leaf, cooked, boiled, drained" has about half as much iron as "Spinach, cooked, boiled, drained". A discrepancy, indeed, though not the same one cited in the question. My interpretation here is that the frozen spinach is simply not cooked in the same way (boiled and drained more thoroughly) as the non-frozen.
An alternative, proposed by Adisak, is that the frozen spinach nutrition means that you've taken the already-cooked, frozen spinach and boiled it again and drained away even more nutrients. This seems unlikely; frozen spinach is already cooked, so there's no reason for the nutrition information to assume that you'll boil it over again. The description (it seems to me) is referring to the cooking that took place before it was frozen.
Best Answer
So, there's maybe a few things I found to reduce the astringency or bitterness of spinach. If you can reduce the bitterness to a flavor you like first, rather then relying on the sugar to mask or balance astringency (which it doesn't hide so much) - you can probably end up with a better dessert.
One thought is that blanching the spinach will help counter bitterness. briefly boil your washed spinach, and discard the water. If you're intending to further cook the spinach afterwards (as in making a fruit-based halwa), cold shocking it might not be needed - It's possible that discarding the water will be enough, though of course you can try with and without the cold shock to see what works for you.
Another thing is astringency can be countered or hidden by soaking in different substances - Adding a bit of milk or fats to your final recipe (as in some of the fattier nut-style halwas) should help balance a little bitterness, Pre-soaking the spinach in milk and discarding might work to draw out some of the astringency. Soaking in food grade lime or absorbic acid like lemon juice or vitamin C, might also work.
Another option is to consider the source of your spinach - fresh baby spinach (for example) will likely not have as much of the bitterness in it to begin with, compared to a cooked full grown spinach. Baby spinach is mild enough to be eaten straight in a salad, mild enough that it might even be candied, like rose petals, for a garnish after your dish is complete.
You might also consider whether the spinach will work better as a flavoring agent or as a bulk agent in your halwa - many fruit based halwas (which seems the easiest method) simply stew the fruit with sugar for a long cooking period, so you need to make sure the spinach as a whole is not going to turn bitter or change while cooking. Other types of halwa may use different ingredients, for different effects - a jelly based or nut-based halwa might easily be flavored with spinach juice... juice which can be extracted at any point along the process, from raw to well-boiled. Leaving the solids behind may help reduce unwanted flavors - or just make the juice more controllable (that is, extract the juice when it is a flavor you like, and the lack of the rest of the plant might keep it form changing overmuch).
You might even consider pairing your spinach with another fruit or vegetable, something complementary or neutral for the bulk removed if you go the juice route - something mild and vegetal might mellow the spinach taste without overriding it (especially if you watch the proportions and use more spinach flavor, less other flavors). Maybe watercress, or celery, asparagus, or bellpepper, something like that that tastes green, or tastes good with spinach. Or you could find a flavor that goes well with the spinach - citrus, or apple, or berries - the kind of flavors that show up on sweet dressings for fresh spinach salads.