The company I work for sent me a check which on which the bank issued a 10-day hold on after I deposited it saying that the account had been frozen.

The company says things are fine but I am concerned. Should I be worried about their solvency?

If there accounts are frozen for the company most likely they are involved in a law suit or other banking issue.
If your company pay check is not clearing the bank, yes that is something to be worried about.

I find your question interesting. Assuming the check was not drawn off your particular bank, it is common to have an extended hold, as there is no immediate recourse. However, it would be a complete violation of privacy laws for bank ABC to state the current financial/legal standings of another's account, this includes consumer and business accounts alike. Secondly, if the business account was frozen, you would not be instructed of a hold, you would be instructed that the bank is unable to credit your account for the check. The bank would then refer you to the remitter, and, by law, provide no more or less info.