A couple things could be happening. The first one that comes to mind is that the marks may have been first hidden by the dirt, then hidden by the wetness of the washing. The material typically turns darker when it is wet and that could easily hide the marks, if they are white. It does not mean that the blanket is damaged unless the marks are also holes.
The 2nd possibility is that your washing machine may not be big enough for the larger blankets, which are rubbing on the sides of the tub. What kind of washing machine are you using? I used one of the over-sized non-commercial front loaders for about 8 years, but I was not warned when I bought it that all of these big front loaders do the spin cycles with the tub at a right angle to the ground, and that every one of these machines is intentionally designed so that they will only last 6 – 8 years, and that is without washing anything as heavy as larger horse blankets. The washing machine makers only make money if we consumers have to replace the washing machine, so they intentionally designed these machines so that the bearings will wear out, and are so placed that it costs almost as much to replace the machine than to repair it, as the entire machine has to be disassembled to get to the bearings. Planned obsolescence at its worst. So this year I will bite the bullet and find a used commercial machine. And I would not recommend that anyone buy these machines even if only to wash their own clothes.
As long as the white streaks do not result in holes, you should be fine. Blankets should be re-waterproofed once a year, and the best waterproofing I have found is the one Wall-Mart sells in the camping section, the one with the orange cap that costs right around $5 per can. For a 78, you will need approximately 3 cans, depending on how much of the old factory applied top layer is still intact. What destroys the top layer waterproofing is UV rays, and there is no real way to protect the blanket from UV rays, since the t/O blankets are designed for the the horse to be turned out in. But there is a 2nd part of the waterproofing, and that is the membrane that is laminated to the underside of the top layer. As long as this membrane is intact, you can replay the blankets and they will be waterproof. But the UV rays do penetrate the blanket, and will eventually cause the membrane to de-laminate, and at that point, respraying the top layer will not be enough, and your T/O becomes a stall blanket or a blanket liner.
The blanket makers seldom release this type of info, and most horse people, even the experienced ones who have horses all their lives don’t know this. I know it because I repair horse blankets and I buy rolls of the same material the blanket makers use both for repairs, and for mini T/O’s, and the people who sell the material are a bit more forth-coming about what makes the T/O’s waterproof. Especially if one manages to ask the right questions.
Hope this helps.