I would say she is a 3 on the scale
The Henneke scale perhaps? If she's a 3 on that, she obviously needs to gain some, but I wouldn't call that 'very skinny'. But either way, it's also not great to try to 'bulk them up' too quickly, even if they're extremely poor - gradual weight gain is healthiest.
feeding her 1lb of feed 2x a day. I have been feeding a mix of cracked corn, oats, molasses from my feed store.
What was the previous owner feeding her? Did you build up to that? It's always best to change/add/remove different ingredients gradually.
Please learn more about equine digestion & feeding & seriously reconsider feeding this sort of 'junk food'. Horses don't do well on high starch/sugar feeds, so grain is generally not the best option. If deemed necessary, oats are a good grain, easily digested & (relatively) low in starch, but corn is about the worst - very high starch & indigestible in the horse's stomach. Molasses is high sugar & low anything else. The problems of indigestible and high starch feeds are exacerbated when they're fed infrequently rather than little & often. Small, high fibre, frequent meals are best. Not that 1lb is much, but...
With that diet, especially if that's what she has been fed long term, I wouldn't be surprised she's not doing well & I'd also be considering an ulcer treatment &/or probiotic. I'd be feeding her a healthy alternative
getting about 10lbs of grass hay 2x a day as well. She is also allowed free pasture all day and I have been considering letting her out at night as well.
Yep, 20lb daily should be a good maintenance amount for a 1000lb horse & if she's also getting grass, that should probably be OK. The guideline is that horses need an absolute minimum of 1.5% bwt daily in forage, at least 2.5-3% or free choice for maintenance or weight gain. Their system doesn't cope well with periods of hunger - they're built for little & near constant feeding - so I'd ensure she had adequate hay over night especially, &/or don't lock her up. It's not good to coop horses up for a number of health(& wellbeing) reasons, including digestive issues from lack of free movement &/or stress.
I have purchased a round of wormer for her but am afraid to give it just yet. I have arranged for the farrier to come out tomorrow to take care of her hooves. Vet check shows everything is ok, teeth, blood work, etc. I purchased a bag of beet pulp but am unsure how to or if I should even feed it.
Yes, effective worming & teeth maintenance are very important to enable horses to get the most from their feed too. Why are you frightened to give the wormer? Are you inexperienced, never done it before? If so, I'd suggest finding someone experienced to help & teach you(if you need the vet again, get him to give it, while you're paying him for being there anyway
Beet pulp is a good high energy feed, being also low sugar & high fibre. As mentioned, start anything like this gradually - you could start with a cup(dry, before soaking) per day divided over the meals, increasing every couple of days until you get to about 4-6 cups daily(will make 8-12 cups soaked). Other high energy options are alfalfa chaff or hay, rice bran, soy hulls, etc.
The other thing to consider is her nutrition. If her diet is imbalanced/lacking in certain nutrients - which they almost invariably are in something or other - she may be failing to thrive due to nutrition rather than lack of calories.