XOR-CBC offers little to no protection, especially against known plaintext.
Let's take the definition of the question:
For $i=0$:
$$C_{i=0} \equiv \left(\bigoplus_{IV}^{P_{i=0}}\right) \oplus {K}$$
for $i \ge 1$:
$$C_i \equiv \left(\bigoplus_{C_{i-1}}^{P_i}\right) \oplus {K}$$
then an iteration for a given $i$ of XOR-CBC encryption is, for $i \ge 1$:
$$C_i = \operatorname{E}(K, C_{i-1} \oplus P_i) \to$$
$$C_i = K \oplus (C_{i-1} \oplus P_i)$$
The block size is necessarily the same size as the key size in this scheme.
Then let's show that the value of $K$ is immediately leaked if a single $P_i$ for a specific $i$ is known:
$$K = (C_{i-1} \oplus P_{i}) \oplus C_{i}$$
You simply XOR both sides with $K$ and then with $C_{i}$ to get to this equation, in case your math is rusty.
As the IV is generally known, information about the first plaintext block equality leaks information about the key.
Even worse, you can perform that attack for any known bit $b$ for any iteration, and you can combine those known bits of a key to find a full key, or to bruteforce the rest of the key.
$$C_{i,b} = K_b \oplus (C_{i-1,b} \oplus P_{i,b})$$
Now assume that $P_{i,b}$ is known (known plaintext) and $C_{i-1,b}$ is known, then $K_b$ is immediately known as:
$$K_b = (C_{i-1,b} \oplus P_{i,b}) \oplus C_{i,b}$$
Since the key is repeated, the above equation holds for any bit in the key: known plaintext at the same location (modulus the block / key size) will immediately expose the key bit at the same location within the block.
This is the original stronger attack that I had shown, which is slightly more complex and confusing. I showed it to indicate that known even a single bit of known plaintext already breaks the cipher. Each bit in the ciphertext only depends on a single bit of the key instead of all bits - as usual for ciphers!
The security in CBC relies for a large part on the protection of the key value that the block cipher offers. If that protection is taken away, then CBC mode - and most if not all other block cipher modes - will fail.
Also compare XOR-CBC with a one-time-pad where the key bits become known if the plaintext is known. For an OTP though the key stream should never repeat, so the the knowledge of the key bits doesn't expose any other information. XOR-CBC implies the reuse of the bits in the key.
So you don't even need "advanced" analysis like in tylo's answer. Commonly ciphers are required to be secure under for known- and even chosen plaintext and CBC clearly doesn't hold under assumption if XOR is used instead of a block cipher.