There is no evidence yet the deer actually get sick. It's quite normal for a virus to be terribly pathogenic in one mammalian species, and able to infect a wide variety of others but without illness or only minor illness. For example, camelpox (related to smallpox) is horrible in camels and kills a quarter of camels infected. In humans and most other mammals it usually is limited to skin sores at the site of contact and goes away quickly. Similarly, monkeypox is highly contagious and usually fatal in its host monkeys, much less contagious and only infrequently fatal in humans, and downright hard to give to a cow or mouse and it won't make them ill. But they can catch it. All of the poxes exhibit that trait, with family- or genus-specific pathogenicity but broad cross-species contagiousness.