You really aren't giving up much. In New York, you don't have the right to sue an employer, as injury or death that happens while you're working is covered by worker's compensation. Moreover, to the limited extent that you can sue an employer i.e. for intentional conduct, such a waiver would likely be deemed ineffective.
Before signing, you may wish to confirm that you'll be covered under the worker's compensation policy, and if so, then I don't think you should worry about it.
It sounds like the waiver that ski areas have on the back of their tickets. But you cannot sue your employer anyway, other than through workers' comp. You might want to consult an attorney who can talk to their lawyer about slightly modifying the language.
A local long time doctor around here, on the verge of retirement no less, got kicked and killed by a horse. It's inherently dangerous, and you understand that already. Horse pucky happens. However, if your employer is "grossly negligent" under the law or does something intentional to harm you, you can sue them despite the release. Although you should always have an attorney review a contract before you sign it (ounce of prevention vs. a pound of cure), these are the types of documents one would expect you to sign in these situations.
This response does not create an attorney-client relationship and is not intended to provide legal advice for your specific situation.