I have done it in 57 bytes

[AkosMaster]

Reddit wont allow me to comment :(

Here u go with 57 bytes: (hope it really is, I dont have much experience but windows says its 57 bytes)
(xor ax, ax instead of mov ax, 0)

; register usage during main loop
; DS: 0xB800, segment of screen buffer
; BX: 0x7D0, screen size (40x25x2 bytes), used in food generation, edge checks, also used for screen accesses but constantly reinitialized
; DI: position of the snake head
; SI: pointer to memory location where the current position of the snake head is stored (actual pointer is BP+SI because it defaults to SS)
lds si, [bx+si] ; SI=0x100 and BX=0x0 at program start in most DOS versions, this initializes DS and SI (machine code at 0x100 is c5 30 00 b8)
db 0x0 ; dummy byte for LDS. this with 'mov ax, 0x0' is actually 'add [bx+si+0x0], bh' but player dies immediately and loop returns to start
start: ; reset game

xor ax, ax          ;  (use xor ax, ax instead of mov ax, 0 - DuczAkos)  set video mode (AH=0x00) to mode 0 (AL=0x0), text mode 40x25 16 colors
int 0x10            ;     using BIOS interrupt call, also clears the screen
mov di, [bx]        ;   reset head position, BX always points to a valid screen position containing 0x720 after setting video mode
lea sp, [bp+si]     ;   set stack pointer (tail) to current head pointer

.food: ; create new food item
in ax, 0x40 ; read 16 bit timer counter into AX for randomization
and bx, ax ; mask with BX to make divisible by 4 and less than or equal to screen size
xor [bx], cl ; place food item and check if position was empty by applying XOR with CL (assumed to be 0xFF)
.input: ; handle keyboard input
mov bx, 0x7D0 ; initialize BX
jp .food ; if position was occupied by snake or wall in food generation => try again, if we came from main loop PF=0
in al, 0x60 ; read scancode from keyboard controller - bit 7 is set in case key was released
imul ax, BYTE 0xA ; we want to map scancodes for arrow up (0x48/0xC8), left (0x4B/0xCB), right (0x4D/0xCD), down (0x50/0xD0) to movement offsets
aam 0x14 ; IMUL (AH is irrelevant here), AAM and AAD with some magic constants maps up => -80, left => -2, right => 2, down => 80
aad 0x44 ; using arithmetic instructions is more compact than checks and conditional jumps
cbw ; but causes weird snake movements though with other keys
add di, ax ; add offset to head position
cmp di, bx ; check if head crossed vertical edge by comparing against screen size in BX
lodsw ; load 0x2007 into AX from off-screen screen buffer and advance head pointer
adc [di], ah ; ADC head position with 0x20 to set snake character
jnp start ; if it already had snake or wall in it or if it crossed a vertical edge, PF=0 from ADC => game over
mov [bp+si], di ; store head position, use BP+SI to default to SS
jz .food ; if food was consumed, ZF=1 from ADC => generate new food
.wall: ; draw an invisible wall on the left side
mov [bx], cl ; store wall character
sub bx, BYTE 0x50 ; go one line backwards
jns .wall ; jump to draw the next wall
pop bx ; no food was consumed so pop tail position into BX
mov [bx], ah ; clear old tail position on screen
jnp .input ; loop to keyboard input, PF=0 from SUB

[AkosMaster]

Yey the formatting went wrong somehow

[donno2048]

It won't work, the bytes encoding the mov are used to initialize es with lds.

This is also explained in the comment.

[AkosMaster]

Oops
I tested it on the wrong file lol