On the level of general philosophy, Burkean conservatism is little more than a statement of the precautionary principle. "Don't change anything, because you never know what kind of chaos it could unleash." That's profoundly risk-averse.
Economics are where we most often hear pro-risk rhetoric from conservatives, as they praise the virtues of the market and the entrepreneur. But I could count the GOP's real libertarians on one hand. Modern conservative economic policy is aimed at reducing risks to corporations, through a combination of deregulation and corporate welfare. (Note, for example, that Bush's one genuine environmental accomplishment, the regulations on off-road diesel emissions, was implemented because the affected corporations wanted to get a uniform law on the books already to reduce their uncertainty.) The fact that these policies shift risk onto consumers and workers is a side effect, not a goal.
In foreign policy, conservatism frames itself as protection from risk. The risk of terrorism or weapons of mass destruction is a motivating principle for conservative policy. (There's a nice synergy here, as the defense spending needed to protect us from the risk of terrorism and WMDs goes to keep various corporations afloat.)
In social policy conservatism is at its most risk-averse. Conservative social policy aims at having a place for everyone and everyone in their place. Much of it is motivated by the desire to have clearly prescribed roles for everyone (particularly with respect to gender), to reduce the uncertainties of social interaction. Practices that violate this order, such as homosexuality, are feared as bringers of disruption and chaos. Conservative religion places supreme value on the certainty of divine revelation, and evangelism aims to spread that committment to all of society. Media censorship reduces the risk that children may be exposed to material that their parents don't approve of.
Even Social Security reform can be understood as risk-aversion. The justification for private accounts is not the bracing effects of exposing your retirement to the risks of the stock market. Rather, it's the percieved riskiness of the status quo. Pro-privatization arguments emphasize the government's untrustworthiness. Keeping your retirement money in your own hands, then, sounds like a recipe for safety.
All this is not to say that liberals are basically risk-seeking. Both philosophies are basically risk-averse, but in different ways. They just emphasize different risks.