My question would be are you planning to leave the cattle on it after seeding? If so no point in seeding cause the root system will be weak and they will just pull it up as they graze. If you are going to plant it then take off for a long while I see no problem with it. Cattle are rough on grass
Since you have pasture divided into 4. I would put cows on 3 sections and I would just plant one section a year and keep them off that one section until the grass heads and falls over and then reseeds itself again and then use it as stock piled forage in the winter. Then plant the next one and do the same thing. You spread out cost and spread out chance of drought and 4 years will fly by quicker than you think in the cattle business. You should be ready to go full bore by the time the next market uptick hits.